Advertisements
Advertisements
प्रश्न
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
9, 8.1, 7.29, ...
Advertisements
उत्तर
Here, a = 9, r = 0.9
Since l r l = | 0.9 | = 0.9 < 1, the sum to infinity of this G.P. exist and
S = `"a"/(1 - "r")`
= `9/(1 - 0.9)`
= `9/0.1`
= 90.
APPEARS IN
संबंधित प्रश्न
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7thterm.
Which term of the following sequence:
`sqrt3, 3, 3sqrt3`, .... is 729?
Find:
the ninth term of the G.P. 1, 4, 16, 64, ...
The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Find the sum of the following geometric progression:
1, −1/2, 1/4, −1/8, ... to 9 terms;
Find the sum of the following geometric progression:
4, 2, 1, 1/2 ... to 10 terms.
Find the sum of the following geometric series:
`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;
Find the sum of the following geometric series:
\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]
Evaluate the following:
\[\sum^n_{k = 1} ( 2^k + 3^{k - 1} )\]
The 4th and 7th terms of a G.P. are \[\frac{1}{27} \text { and } \frac{1}{729}\] respectively. Find the sum of n terms of the G.P.
If a and b are the roots of x2 − 3x + p = 0 and c, d are the roots x2 − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.
Express the recurring decimal 0.125125125 ... as a rational number.
Find the rational numbers having the following decimal expansion:
\[0 . \overline3\]
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
If a, b, c are in G.P., prove that:
\[\frac{(a + b + c )^2}{a^2 + b^2 + c^2} = \frac{a + b + c}{a - b + c}\]
If a, b, c are in G.P., prove that:
(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.
If (a − b), (b − c), (c − a) are in G.P., then prove that (a + b + c)2 = 3 (ab + bc + ca)
If a, b, c are in G.P., then prove that:
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
If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then P2 is equal to
The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
The two geometric means between the numbers 1 and 64 are
If for a sequence, tn = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio
Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1
For a G.P. If t4 = 16, t9 = 512, find S10
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`1/2, 1/4, 1/8, 1/16,...`
Select the correct answer from the given alternative.
The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –
The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is ______.
Answer the following:
For a sequence , if tn = `(5^("n" - 2))/(7^("n" - 3))`, verify whether the sequence is a G.P. If it is a G.P., find its first term and the common ratio.
Answer the following:
If for a G.P. t3 = `1/3`, t6 = `1/81` find r
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is ______.
The sum or difference of two G.P.s, is again a G.P.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
