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 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
Find the value of n so that `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.
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.
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
Find:
the ninth term of the G.P. 1, 4, 16, 64, ...
Which term of the G.P.: `sqrt3, 3, 3sqrt3`, ... is 729?
In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.
If \[\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}\] (x ≠ 0), then show that a, b, c and d are in G.P.
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 series:
0.6 + 0.66 + 0.666 + .... to n terms
Find the sum of the following serie to infinity:
`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
Prove that: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.
Find k such that k + 9, k − 6 and 4 form three consecutive terms of a G.P.
If a, b, c are in G.P., prove that:
\[\frac{1}{a^2 - b^2} + \frac{1}{b^2} = \frac{1}{b^2 - c^2}\]
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 three distinct real numbers in G.P. and a + b + c = xb, then prove that either x< −1 or x > 3.
If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]
Find the geometric means of the following pairs of number:
2 and 8
Find the geometric means of the following pairs of number:
a3b and ab3
If pth, qth and rth terms of a G.P. re x, y, z respectively, then write the value of xq − r yr − pzp − q.
The two geometric means between the numbers 1 and 64 are
The number of bacteria in a culture doubles every hour. If there were 50 bacteria originally in the culture, how many bacteria will be there at the end of 5th hour?
The numbers 3, x, and x + 6 form are in G.P. Find x
The numbers 3, x, and x + 6 form are in G.P. Find nth term
Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 10 years.
A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball
Find GM of two positive numbers whose A.M. and H.M. are 75 and 48
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
Select the correct answer from the given alternative.
The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –
Select the correct answer from the given alternative.
If common ratio of the G.P is 5, 5th term is 1875, the first term is -
Answer the following:
In a G.P., the fourth term is 48 and the eighth term is 768. Find the tenth term
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:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
Answer the following:
If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2
Answer the following:
If p, q, r, s are in G.P., show that (pn + qn), (qn + rn) , (rn + sn) are also in G.P.
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.
