Advertisements
Advertisements
Question
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Solution
Let the sum of n terms of the G.P. be 315.
It is known that, Sn `(a(r^n - 1))/(r - 1)`
given geometric progression
5 + 10 + 20 + 40 + …….
Sum of n terms = `(5(2^"n" - 1))/(2 -1) = 315`
∴ 2n – 1 = 63
or 2n = 64 = 26
n = 6
6th term = 5 × 26 – 1
= 5 × 25
= 5 × 32
= 160
APPEARS IN
RELATED QUESTIONS
Which term of the following sequence:
`1/3, 1/9, 1/27`, ...., is `1/19683`?
For what values of x, the numbers `-2/7, x, -7/2` are in G.P?
The sum of first three terms of a G.P. is `39/10` and their product is 1. Find the common ratio and the terms.
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn
If a, b, c are in A.P,; b, c, d are in G.P and ` 1/c, 1/d,1/e` are in A.P. prove that a, c, e are in G.P.
Find the 4th term from the end of the G.P.
\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]
Find the sum of the following serie:
5 + 55 + 555 + ... to n terms;
Find the sum of the following series:
0.6 + 0.66 + 0.666 + .... to n terms
How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?
The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.
Find the sum :
\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]
If S1, S2, S3 be respectively the sums of n, 2n, 3n terms of a G.P., then prove that \[S_1^2 + S_2^2\] = S1 (S2 + S3).
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
Express the recurring decimal 0.125125125 ... as a rational number.
If S denotes the sum of an infinite G.P. S1 denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively
\[\frac{2S S_1}{S^2 + S_1}\text { and } \frac{S^2 - S_1}{S^2 + S_1}\]
Three numbers are in A.P. and their sum is 15. If 1, 3, 9 be added to them respectively, they form a G.P. Find the numbers.
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.
If a, b, c, d are in G.P., prove that:
(a2 + b2 + c2), (ab + bc + cd), (b2 + c2 + d2) are in G.P.
If \[\frac{1}{a + b}, \frac{1}{2b}, \frac{1}{b + c}\] are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.
If a, b, c are three distinct real numbers in G.P. and a + b + c = xb, then prove that either x< −1 or x > 3.
Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .
If A1, A2 be two AM's and G1, G2 be two GM's between a and b, then find the value of \[\frac{A_1 + A_2}{G_1 G_2}\]
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
The fractional value of 2.357 is
If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is
Check whether the following sequence is G.P. If so, write tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
For the following G.P.s, find Sn
3, 6, 12, 24, ...
For a G.P. a = 2, r = `-2/3`, find S6
Find the sum to n terms of the sequence.
0.5, 0.05, 0.005, ...
Select the correct answer from the given alternative.
Sum to infinity of a G.P. 5, `-5/2, 5/4, -5/8, 5/16,...` is –
Select the correct answer from the given alternative.
Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively. (a, b > 0)
Answer the following:
Find three numbers in G.P. such that their sum is 35 and their product is 1000
Answer the following:
If a, b, c are in G.P. and ax2 + 2bx + c = 0 and px2 + 2qx + r = 0 have common roots then verify that pb2 – 2qba + ra2 = 0
In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is ______.
The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252cm2. The length of the longest edge is ______.
The sum or difference of two G.P.s, is again a G.P.
