Solution
The sum of n terms of an A.P. is 2n². Find the 5th term.
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 25: Arithmetic and Geometric Progressions
Which term of the series 1, 2, 4, 8, ... is 256?
Problem 35: Arithmetic and Geometric Progressions
Sum the following series: 1 1/2 + 2 1/4 + 3 3/8 + ------------- to 8 terms.
Problem 27: Arithmetic and Geometric Progressions
Find n if 1/217 is the nth term of the series 16, 8, 4, ...?
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 64 : Arithmetic and Geometric Progressions
A manufacturer reckons that the value of the machine costing him $18,750 depreciates each year by 20...
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 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 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 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 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 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 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 - -----------.
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 40: Arithmetic and Geometric Progressions
Sum the n terms series: (a + b) + (a2 + 2b) + (a3 + 3b) + -----------.
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 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 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 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 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 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 34: Arithmetic and Geometric Progressions
Sum the following series: 1 - 1/2 + 1/4 - 1/8 + ------------- to 12 terms.
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
If 10th term of an A.P. is 15 and the 15th term is 10, find the series.
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Problem 11: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
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 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 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 37: Arithmetic and Geometric Progressions
Sum the n terms series: 1/√3 + 1 + 3√3 + -----------.
Problem 39: Arithmetic and Geometric Progressions
Sum the n terms series: 0.3 + 0.03 + 0.003 + -----------.
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 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 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 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 33: Arithmetic and Geometric Progressions
Sum the following series: 1024 + 512 + 256 + ------------- to 15 terms.
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 16: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
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 26: Arithmetic and Geometric Progressions
Is 1/3125 a term of the series 25, 5, 1,...?
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 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 15: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
Minhajur Rahaman
