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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
Arithmetic and Geometric Progressions
Problem 37: Arithmetic and Geometric Progressions
Sum the n terms series: 1/√3 + 1 + 3√3 + -----------.
Problem 47: Arithmetic and Geometric Progressions
Find the infinite G.P. whose first term is 1/4 and the sum is 1/3.
Problem 12: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
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 25: Arithmetic and Geometric Progressions
Which term of the series 1, 2, 4, 8, ... is 256?
Problem 38: Arithmetic and Geometric Progressions
Sum the n terms series: 2 1/2 - 1 + 2/5 - -----------.
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 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 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 49: Arithmetic and Geometric Progressions
Find three numbers in G.P. such that their sum is 130, and their product is 27,000.
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 35: Arithmetic and Geometric Progressions
Sum the following series: 1 1/2 + 2 1/4 + 3 3/8 + ------------- to 8 terms.
Problem 26: Arithmetic and Geometric Progressions
Is 1/3125 a term of the series 25, 5, 1,...?
Problem 33: Arithmetic and Geometric Progressions
Sum the following series: 1024 + 512 + 256 + ------------- to 15 terms.
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 16: Arithmetic and Geometric Progressions
If a, b, c are in G.P., prove that a(b2+c2)=c(a2+b2)
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
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 36: Arithmetic and Geometric Progressions
Sum the following series: √2 + √6 + √18 + ------------- to 10 terms.
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 39: Arithmetic and Geometric Progressions
Sum the n terms series: 0.3 + 0.03 + 0.003 + -----------.
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 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 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...
If 10th term of an A.P. is 15 and the 15th term is 10, find the series.
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Problem 27: Arithmetic and Geometric Progressions
Find n if 1/217 is the nth term of the series 16, 8, 4, ...?
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 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 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 40: Arithmetic and Geometric Progressions
Sum the n terms series: (a + b) + (a2 + 2b) + (a3 + 3b) + -----------.
Minhajur Rahaman
