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

Problem 40: Arithmetic and Geometric Progressions

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

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 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 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 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 12: 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 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 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 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 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

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

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 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 34: Arithmetic and Geometric Progressions

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

Problem 38: Arithmetic and Geometric Progressions

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

Problem 11: Arithmetic and Geometric Progressions

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

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 13: Arithmetic and Geometric Progressions

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

Problem 49: Arithmetic and Geometric Progressions

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

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 36: Arithmetic and Geometric Progressions

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

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 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

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,...?

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

E1: Which term of series

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

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 47: Arithmetic and Geometric Progressions

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

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

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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 16: Arithmetic and Geometric Progressions

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

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...

Arithmetic and Geometric Progressions

Arithmetic and Geometric Progressions

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