Arithmetic and Geometric Progressions

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

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

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

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

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

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

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

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

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

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

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Arithmetic and Geometric Progressions

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

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 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.

E1: Which term of series

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

Problem 12: 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 26: Arithmetic and Geometric Progressions

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

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 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 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 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...

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

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 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) + -----------.

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

Problem 35: Arithmetic and Geometric Progressions

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

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 13: Arithmetic and Geometric Progressions

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

Problem 27: Arithmetic and Geometric Progressions

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

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 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 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...

Arithmetic and Geometric Progressions

Arithmetic and Geometric Progressions

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