Advertisements
Advertisements
प्रश्न
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 –
पर्याय
5
`-1/2`
`10/3`
`3/10`
Advertisements
उत्तर
Sum to infinity of a G.P. 5, `-5/2, 5/4, -5/8, 5/16,...` is `10/3`
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`1/3, 1/9, 1/27`, ...., is `1/19683`?
Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).
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 four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
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.
If a and b are the roots of are roots of x2 – 3x + p = 0 , and c, d are roots of x2 – 12x + q = 0, where a, b, c, d, form a G.P. Prove that (q + p): (q – p) = 17 : 15.
Find :
nth term of the G.P.
\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]
The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
Find three numbers in G.P. whose sum is 38 and their product is 1728.
Find the sum of the following geometric progression:
(a2 − b2), (a − b), \[\left( \frac{a - b}{a + b} \right)\] to n terms;
Find the sum of the following geometric series:
\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8 terms };\]
Find the sum of the following geometric series:
(x +y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + ... to n terms;
Find the sum of the following geometric series:
x3, x5, x7, ... to n terms
Evaluate the following:
\[\sum^{10}_{n = 2} 4^n\]
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.
How many terms of the G.P. `3, 3/2, 3/4` ..... are needed to give the sum `3069/512`?
If S1, S2, ..., Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ..., n respectively, then prove that S1 + S2 + 2S3 + 3S4 + ... (n − 1) Sn = 1n + 2n + 3n + ... + nn.
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: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.
The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
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.
Find the geometric means of the following pairs of number:
−8 and −2
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
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 a G.P. If t4 = 16, t9 = 512, find S10
Find the sum to n terms of the sequence.
0.2, 0.02, 0.002, ...
Select the correct answer from the given alternative.
The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –
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
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
Let `{a_n}_(n = 0)^∞` be a sequence such that a0 = a1 = 0 and an+2 = 2an+1 – an + 1 for all n ≥ 0. Then, `sum_(n = 2)^∞ a^n/7^n` is equal to ______.
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 ______.
For an increasing G.P. a1, a2 , a3 ........., an, if a6 = 4a4, a9 – a7 = 192, then the value of `sum_(i = 1)^∞ 1/a_i` is ______.
