Advertisements
Advertisements
प्रश्न
Find :
the 8th term of the G.P. 0.3, 0.06, 0.012, ...
उत्तर
Here,
\[\text { First term }, a = 0 . 3\]
\[\text { Common ratio }, r = \frac{a_2}{a_1} = \frac{0 . 06}{0 . 3} = 0 . 2\]
\[ \therefore 8th\text { term } = a_8 = a r^{(8 - 1)} = 0 . 3(0 . 2 )^7 \]
\[\text { Thus, the 8th term of the given GP is } 0 . 3(0 . 2 )^7 .\]
APPEARS IN
संबंधित प्रश्न
Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`
Which term of the following sequence:
`1/3, 1/9, 1/27`, ...., is `1/19683`?
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.
If the pth , qth and rth terms of a G.P. are a, b and c, respectively. Prove that `a^(q - r) b^(r-p) c^(p-q) = 1`
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.
Which term of the G.P. :
\[2, 2\sqrt{2}, 4, . . .\text { is }128 ?\]
The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.
In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.
The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is \[87\frac{1}{2}\] . Find them.
Find the sum of the following geometric series:
\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8 terms };\]
Evaluate the following:
\[\sum^{10}_{n = 2} 4^n\]
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.
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Find the common ratio of the G.P.
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
Find the rational numbers having the following decimal expansion:
\[0 .\overline {231 }\]
Find the rational numbers having the following decimal expansion:
\[3 . 5\overline 2\]
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:
\[\frac{1}{a^2 - b^2} + \frac{1}{b^2} = \frac{1}{b^2 - c^2}\]
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
If a, b, c are in A.P. and a, b, d are in G.P., show that a, (a − b), (d − c) are in G.P.
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
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 p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to
For the G.P. if a = `7/243`, r = 3 find t6.
For the G.P. if a = `2/3`, t6 = 162, find r.
The numbers 3, x, and x + 6 form are in G.P. Find nth term
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.
Find: `sum_("r" = 1)^10(3 xx 2^"r")`
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.
Select the correct answer from the given alternative.
Which term of the geometric progression 1, 2, 4, 8, ... is 2048
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:
If pth, qth and rth terms of a G.P. are x, y, z respectively. Find the value of xq–r .yr–p .zp–q
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.
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 ______.
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 ______.