Advertisements
Advertisements
प्रश्न
The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.
Advertisements
उत्तर
Here, a = 3
Common ratio,r = 3
Sum of n terms, Sn = 381
∴ Sn = 3 + 6 + 12 + ... + n terms
\[\Rightarrow 381 = 3\left( \frac{2^n - 1}{2 - 1} \right) \]
\[ \Rightarrow 381 = 3 \left( 2^n - 1 \right)\]
\[ \Rightarrow 127 = 2^n - 1\]
\[ \Rightarrow 2^n = 128 \]
\[ \Rightarrow 2^n = 2^7 \]
\[ \therefore n = 7\]
संबंधित प्रश्न
For what values of x, the numbers `-2/7, x, -7/2` are in G.P?
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
Evaluate `sum_(k=1)^11 (2+3^k )`
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.
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
Find:
the ninth term of the G.P. 1, 4, 16, 64, ...
Which term of the G.P. :
\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]
The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.
The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.
Evaluate the following:
\[\sum^{11}_{n = 1} (2 + 3^n )\]
How many terms of the sequence \[\sqrt{3}, 3, 3\sqrt{3},\] ... must be taken to make the sum \[39 + 13\sqrt{3}\] ?
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 of the following serie to infinity:
`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`
Find the sum of the following series to infinity:
`1/3+1/5^2 +1/3^3+1/5^4 + 1/3^5 + 1/56+ ...infty`
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
If Sp denotes the sum of the series 1 + rp + r2p + ... to ∞ and sp the sum of the series 1 − rp + r2p − ... to ∞, prove that Sp + sp = 2 . S2p.
The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of the succeeding terms. Find the G.P.
Show that in an infinite G.P. with common ratio r (|r| < 1), each term bears a constant ratio to the sum of all terms that follow it.
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
\[\frac{2S S_1}{S^2 + S_1}\text { and } \frac{S^2 - S_1}{S^2 + S_1}\]
Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .
In a G.P. if the (m + n)th term is p and (m − n)th term is q, then its mth term is
For the G.P. if r = `1/3`, a = 9 find t7
Which term of the G.P. 5, 25, 125, 625, … is 510?
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.
For the following G.P.s, find Sn.
`sqrt(5)`, −5, `5sqrt(5)`, −25, ...
For a G.P. If t3 = 20 , t6 = 160 , find S7
Find the sum to n terms of the sequence.
0.5, 0.05, 0.005, ...
Express the following recurring decimal as a rational number:
`51.0bar(2)`
Find GM of two positive numbers whose A.M. and H.M. are 75 and 48
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 –
Answer the following:
Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`
Answer the following:
For a G.P. if t2 = 7, t4 = 1575 find a
Answer the following:
If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2
The third term of a G.P. is 4, the product of the first five terms is ______.
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in ______.
The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
If 0 < x, y, a, b < 1, then the sum of the infinite terms of the series `sqrt(x)(sqrt(a) + sqrt(x)) + sqrt(x)(sqrt(ab) + sqrt(xy)) + sqrt(x)(bsqrt(a) + ysqrt(x)) + ...` is ______.
