Arithmetic and Geometric Progressions

Find the infinite G.P. whose first term is 1/4 and the sum is 1/3.

Read more: Problem 47: Arithmetic and Geometric Progressions

The first term of G.P. exceeds the 2nd term by 2 and the sum to infinity is 50, find the series.

Read more: Problem 48: Arithmetic and Geometric Progressions

Find three numbers in G.P. such that their sum is 130, and their product is 27,000.

Read more: Problem 49: Arithmetic and Geometric Progressions

Find three numbers in G.P. such that their sum is 13/3, and the sum of their squares is 91/9.

Read more: Problem 50: Arithmetic and Geometric Progressions

Find five numbers in G.P., such that their product is 32 and the product of the last two is 108.

Read more: Problem 51: Arithmetic and Geometric Progressions

The continued product of three numbers in G.P. is 27, and the sum of theeir products in pairs is 39. Find the numbers.

Read more: Problem 52: Arithmetic and Geometric Progressions

Three numbers whose sum is 18 are in A.P.; if 2,4,11 are added to them respectively, the resulting numbers are in G.P. Determine the numbers.

Read more: Problem 53: Arithmetic and Geometric Progressions

There are four numbers, the first three are in A.P. and the last three in G.P., the sum of the first and the last is 11, and the sum of the other two is 10, find the numbers.

Read more: Problem 55: Arithmetic and Geometric Progressions

The sum of four numbers is GP. Is 60 and the A.M. between the first and the last is 18. Show that the numbers are 4,8,16,32.

Read more: Problem 57: Arithmetic and Geometric Progressions

If a, b, c are three unequal numbers in A.P. and a, b-a, c-a are in G.P., show that a/1 = b/3 = c/5

Read more: Problem 60 : Arithmetic and Geometric Progressions

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Arithmetic and Geometric Progressions

Problem 47: Arithmetic and Geometric Progressions

Find the infinite G.P. whose first term is 1/4 and the sum is 1/3.

Problem 60 : Arithmetic and Geometric Progressions

If a, b, c are three unequal numbers in A.P. and a, b-a, c-a are in G.P., show that a/1 = b/3 = c/5

Problem 37: Arithmetic and Geometric Progressions

Sum the n terms series: 1/√3 + 1 + 3√3 + -----------.

Problem 43: Arithmetic and Geometric Progressions

In a G.P., the sum of n terms is 255, the last term is 128 and the common ratio is 2, find n.

Problem 13: Arithmetic and Geometric Progressions

If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)

Problem 42: Arithmetic and Geometric Progressions

The sum of n terms of a G.P. whose first term is one and the common ratio is 1/2, is 1 127/128, find...

Problem 38: Arithmetic and Geometric Progressions

Sum the n terms series: 2 1/2 - 1 + 2/5 - -----------.

The sum of n terms of an A.P. is 2n². Find the 5th term.

Problem 31: Arithmetic and Geometric Progressions

If the mth term of a G.P. be n and the nth be m, then that the (m+n)th term is nm/m-n/mn/m-n.

Problem 44: Arithmetic and Geometric Progressions

How many terms of the G.P. 1, 4, 16, ... must be taken to have their sum equal to 341?

Problem 41: Arithmetic and Geometric Progressions

The sum of the first eight terms of a G.P. is five times the sum of the first four terms. Find the c...

Problem 61 : Arithmetic and Geometric Progressions

If a, b, c are in A.P., and a, b, (c+1) are in G.P., show c=(a-b)2

Problem 11: Arithmetic and Geometric Progressions

If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)

Find the 20th term of the A.P. 80, 75, 70, …. Calculate the number of terms required to make the sum equal to zero

Problem 40: Arithmetic and Geometric Progressions

Sum the n terms series: (a + b) + (a2 + 2b) + (a3 + 3b) + -----------.

Problem 27: Arithmetic and Geometric Progressions

Find n if 1/217 is the nth term of the series 16, 8, 4, ...?

Problem 35: Arithmetic and Geometric Progressions

Sum the following series: 1 1/2 + 2 1/4 + 3 3/8 + ------------- to 8 terms.

The 4th term of an A.P. is 64 and the 54th term is -61, Show the 23rd term is 16½

Problem 50: Arithmetic and Geometric Progressions

Find three numbers in G.P. such that their sum is 13/3, and the sum of their squares is 91/9.

Problem 24: Arithmetic and Geometric Progressions

The product of first and second terms of a G.P. is 256 and that of second and third terms is 16. fin...

Problem 39: Arithmetic and Geometric Progressions

Sum the n terms series: 0.3 + 0.03 + 0.003 + -----------.

Problem 10: Arithmetic and Geometric Progressions

Find three numbers in G.P. such that their sum is 21 and the sum of their squares is 189

Problem 53: Arithmetic and Geometric Progressions

Three numbers whose sum is 18 are in A.P.; if 2,4,11 are added to them respectively, the resulting n...

Problem 16: Arithmetic and Geometric Progressions

If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)

Problem 23: Arithmetic and Geometric Progressions

The third term of a G.P. is 2/3 and the 6th term is 2/18, find this 8th term.

Problem 48: Arithmetic and Geometric Progressions

The first term of G.P. exceeds the 2nd term by 2 and the sum to infinity is 50, find the series.

Problem 32: Arithmetic and Geometric Progressions

In a G.P. if the (p+q)th term is m and the (p-q)th term is n, prove that the pth term is √mn

Problem 21: Arithmetic and Geometric Progressions

If the value of Fiat car depreciated by 25 per cent annually, what will be its estimated value at th...

Problem 45: Arithmetic and Geometric Progressions

The ratio of the 4th to the 12th term of a G.P. with positive common ratio is 1/256. If the differen...

Problem 25: Arithmetic and Geometric Progressions

Which term of the series 1, 2, 4, 8, ... is 256?

Problem 34: Arithmetic and Geometric Progressions

Sum the following series: 1 - 1/2 + 1/4 - 1/8 + ------------- to 12 terms.

Problem 69 : Arithmetic and Geometric Progressions

Show that a given sum of money if accumulating at 20 per cent per annum more thasn doubles in 4 yea...

Problem 26: Arithmetic and Geometric Progressions

Is 1/3125 a term of the series 25, 5, 1,...?

Problem 29: Arithmetic and Geometric Progressions

The 4th term of a G.P. is x, the 10th term is y and the 16th term is z. Show that xz=y2

Problem 55: Arithmetic and Geometric Progressions

There are four numbers, the first three are in A.P. and the last three in G.P., the sum of the first...

E1: Which term of series

12+9+6+......... is equal to (i) -30, (ii) -100?

Problem 28: Arithmetic and Geometric Progressions

If the nth term of the series 1, 2, 4, 8, .... be the same as the nth term of the series 256, 128, 6...

Problem 52: Arithmetic and Geometric Progressions

The continued product of three numbers in G.P. is 27, and the sum of theeir products in pairs is 39....

Problem 51: Arithmetic and Geometric Progressions

Find five numbers in G.P., such that their product is 32 and the product of the last two is 108.

Problem 15: Arithmetic and Geometric Progressions

If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)

E3: The pth term of an A.P. is q and the qth term is p. Show that the rth term is p+q-r and the (p+q)th term is zero

Problem 30: Arithmetic and Geometric Progressions

The nth term of a sequence is 2.3n-1, show that it is in G.P. What is the first term and the common ...

Problem 33: Arithmetic and Geometric Progressions

Sum the following series: 1024 + 512 + 256 + ------------- to 15 terms.

The Sum of three numbers in G.P. is 35 and their product is 1000. Find the numbers.

Problem 36: Arithmetic and Geometric Progressions

Sum the following series: √2 + √6 + √18 + ------------- to 10 terms.

Prove that if unity is added to the sum of any number of terms of the A.P. 3, 5, 7, 9,…. The resulting sum is a perfect square.

Problem 64 : Arithmetic and Geometric Progressions

A manufacturer reckons that the value of the machine costing him $18,750 depreciates each year by 20...

If 10th term of an A.P. is 15 and the 15th term is 10, find the series.

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Problem 49: Arithmetic and Geometric Progressions

Find three numbers in G.P. such that their sum is 130, and their product is 27,000.

Problem 46: Arithmetic and Geometric Progressions

The sum of infinite terms in a G.P. is 2 and the sum of their squares is 4/3. Find the series.

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