Advertisements
Advertisements
प्रश्न
The first term of a G.P. is 27 and its 8th term is `1/81`. Find the sum of its first 10 terms.
The first term of a G.P. in 27. If the 8th term be `1/81`, what will be the sum of 10 terms?
उत्तर
Given,
First term, a = 27
8th term = ar7 = `1/81`
n = 10
Now,
`(ar^7)/a = (1/81)/27`
`=> r^7 = 1/2187`
`=> r^7 = (1/3)^7`
`=> r = 1/3` ...(∵ r < 1)
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_10 = (27(1 - (1/3)^10))/(1 - 1/3)`
= `(27(1 - 1/3^10))/(2/3)`
= `(27 xx 3)/2(1 - 1/3^10)`
= `81/2 (1 - 1/3^10)`
संबंधित प्रश्न
Find the 8th term of the sequence:
`3/4, 1 1/2, 3, ..............`
Find the 10th term of the G.P. :
`12, 4, 1 1/3, ................`
Find the next three terms of the sequence :
`sqrt5, 5, 5sqrt(5), .............`
Find the seventh term of the G.P. :
`sqrt(3) + 1, 1, (sqrt(3) - 1)/2, .........`
Q 10.2
Q 10.3
Q 1.2
Q 3.1
Q 6
The first and last term of a Geometrical Progression (G.P.) and 3 and 96 respectively. If the common ratio is 2, find:
(i) ‘n’ the number of terms of the G.P.
(ii) Sum of the n terms.
