Advertisements
Advertisements
प्रश्न
The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is ______.
पर्याय
1
3
8
none of these
Advertisements
उत्तर
The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is 1.
Explanation:
Tn = arn-1 = 128 ...(1)
`S_n = (a(r^n-1))/(r-1)` ...(2)
`=> (128r-a)/(r-1) = 255`
Put r = 2
a = 1
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`2, 2sqrt2, 4,.... is 128`
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 of the products of the corresponding terms of the sequences `2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2`
If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
If f is a function satisfying f (x +y) = f(x) f(y) for all x, y ∈ N such that f(1) = 3 and `sum_(x = 1)^n` f(x) = 120, find the value of n.
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.
If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.
Show that one of the following progression is a G.P. Also, find the common ratio in case:
−2/3, −6, −54, ...
Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?
Find the 4th term from the end of the G.P.
\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]
The sum of first three terms of a G.P. is \[\frac{39}{10}\] and their product is 1. Find the common ratio and the terms.
Find the sum of the following geometric series:
1, −a, a2, −a3, ....to n terms (a ≠ 1)
Find the sum :
\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]
The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.
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).
A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
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.
If a, b, c are in G.P., prove that:
(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.
If a, b, c, d are in G.P., prove that:
(a + b + c + d)2 = (a + b)2 + 2 (b + c)2 + (c + d)2
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
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.
Find the geometric means of the following pairs of number:
−8 and −2
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
The fractional value of 2.357 is
The value of 91/3 . 91/9 . 91/27 ... upto inf, is
In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is
Check whether the following sequence is G.P. If so, write tn.
3, 4, 5, 6, …
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
For the G.P. if a = `7/243`, r = 3 find t6.
For what values of x, the terms `4/3`, x, `4/27` are in G.P.?
Express the following recurring decimal as a rational number:
`51.0bar(2)`
If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.
Answer the following:
For a G.P. if t2 = 7, t4 = 1575 find a
If the sum of an infinite GP a, ar, ar2, ar3, ...... . is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, .... 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 ______.
