Chapter 8
Find the 20th and nth terms of the G.P. 5 5 5 2 4 8, , , ...
x3, x5, x7, ... n terms (if x ≠ ± 1).
Evaluate 11/1 (2 3 )k / k = / +∑ .
| The sum of first three terms of a G .P. is | 39 |
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10 and their product is 1. Find the common ratio and the terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
Given a G.P. with a = 729 and 7 th term 64, determine S7.
Find a G.P. for which sum of the first two terms is - 4 and the fifth term is 4 times the third term.
If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, 1 2.
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn - 1 and A, AR, AR2, … ARn - 1 form a G.P, and find the common ratio.
Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that aq - r b r - pcP - q = 1.
If the first and the nth term of a G .P. are a and b, respectively, and if P is the product of n terms, prove tha t P2 = (ab)n.
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1) th to (2n)th term is 1 nr .
If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = ( ab + bc + cd)2 .
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
| Find the value of n so that | a | b |
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a b / n n n n + ++ + 1 1 may be the geometric mean between a and b.
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio ( ) ( )3 2 2 : 3 2 2+ − .
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A A G A G( )( )± + − .
The 5 th, 8 th and 1 1th terms of a G .P. are p, q and s, respectively . Show that q2 = ps.
| The number of bacteria in a certain culture doubles every hour. If there were | 30 |
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bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?
What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
The 4 th term of a G .P. is square of its second term, and the first term is - 3. Determine its 7 th term.
Which term of the following sequences: (a) 2 2 2 4 is128?, , ,... (b) 3 33 3 is729?, , ,... (c) 1 1 1 1 is3 9 27 19683, , ,... ?
| For what values of x, the numbers | 2 | 7 |
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7 2- , x, - are in G.P.? Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10:
0.15, 0.015, 0.0015, ... 20 terms.
7 , 21, 3 7 , ... n terms.
1, - a, a2, - a3, ... n terms (if a ≠ - 1).