Advertisements
Advertisements
प्रश्न
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…
Advertisements
उत्तर
The given G.P. is 0.15, 0.015, 0.00015,...
First term, a = 0.15
Common ratio, r = `0.015/0.15` = 0.1
Sum of geometric series = `("a"(1 - "r"^"n"))/(1 - "r")`
= `(0.15[1 - (0.1)^20])/(1 - (0.1))`
= `(0.15[1 - (0.1)^20])/0.9`
= `(1 - (0.1)^20)/6`
= `1/6[1 - (0.1)^20]`
APPEARS IN
संबंधित प्रश्न
Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
Which term of the following sequence:
`sqrt3, 3, 3sqrt3`, .... is 729?
Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
The sum of first three terms of a G.P. is `39/10` and their product is 1. Find the common ratio and the terms.
Show that one of the following progression is a G.P. Also, find the common ratio in case:
\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]
Find :
nth term of the G.P.
\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]
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.
Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Find the sum of the following geometric series:
x3, x5, x7, ... to n terms
Find the sum of the following serie:
5 + 55 + 555 + ... to n terms;
How many terms of the sequence \[\sqrt{3}, 3, 3\sqrt{3},\] ... must be taken to make the sum \[39 + 13\sqrt{3}\] ?
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.
Find the sum of 2n terms of the series whose every even term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
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
\[\frac{2S S_1}{S^2 + S_1}\text { and } \frac{S^2 - S_1}{S^2 + S_1}\]
If a, b, c are in G.P., prove that:
a (b2 + c2) = c (a2 + b2)
Insert 6 geometric means between 27 and \[\frac{1}{81}\] .
Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .
Find the geometric means of the following pairs of number:
−8 and −2
The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio `(3+2sqrt2):(3-2sqrt2)`.
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio 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
If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term 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
In a G.P. if the (m + n)th term is p and (m − n)th term is q, then its mth term is
Check whether the following sequence is G.P. If so, write tn.
2, 6, 18, 54, …
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
For the G.P. if r = − 3 and t6 = 1701, find a.
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
9, 8.1, 7.29, ...
If the first term of the G.P. is 16 and its sum to infinity is `96/17` find the common ratio.
The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
Answer the following:
Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
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 ______.
