Find a G.P. whose 3rd and 6th terms are 1 and -1/8, respectively. Write down the 10th term also.
Problem 22: Arithmetic and Geometric Progressions
Arithmetic and Geometric Progressions
Problem 16: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
Problem 15: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
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.
If 10th term of an A.P. is 15 and the 15th term is 10, find the series.
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Problem 64 : Arithmetic and Geometric Progressions
A manufacturer reckons that the value of the machine costing him $18,750 depreciates each year by 20...
Problem 35: Arithmetic and Geometric Progressions
Sum the following series: 1 1/2 + 2 1/4 + 3 3/8 + ------------- to 8 terms.
Problem 33: Arithmetic and Geometric Progressions
Sum the following series: 1024 + 512 + 256 + ------------- to 15 terms.
Problem 57: 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 th...
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 26: Arithmetic and Geometric Progressions
Is 1/3125 a term of the series 25, 5, 1,...?
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 12: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
Problem 38: Arithmetic and Geometric Progressions
Sum the n terms series: 2 1/2 - 1 + 2/5 - -----------.
E2: If a, b, c are the pth, qth and rth terms of an A.p., show that
a(q-r)+b(r-p)+c(p-q)=0
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 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 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 25: Arithmetic and Geometric Progressions
Which term of the series 1, 2, 4, 8, ... is 256?
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 40: Arithmetic and Geometric Progressions
Sum the n terms series: (a + b) + (a2 + 2b) + (a3 + 3b) + -----------.
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 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 11: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
Problem 34: Arithmetic and Geometric Progressions
Sum the following series: 1 - 1/2 + 1/4 - 1/8 + ------------- to 12 terms.
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 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 37: Arithmetic and Geometric Progressions
Sum the n terms series: 1/√3 + 1 + 3√3 + -----------.
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 47: Arithmetic and Geometric Progressions
Find the infinite G.P. whose first term is 1/4 and the sum is 1/3.
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 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 27: Arithmetic and Geometric Progressions
Find n if 1/217 is the nth term of the series 16, 8, 4, ...?
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...
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 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 13: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
Problem 22: Arithmetic and Geometric Progressions
Find a G.P. whose 3rd and 6th terms are 1 and -1/8, respectively. Write down the 10th term also.
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 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.
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 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 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
Minhajur Rahaman
