Advertisements
Advertisements
प्रश्न
Find the geometric progression with 4th term = 54 and 7th term = 1458.
Advertisements
उत्तर
Let the first term of the G.P. be a and its common ratio be r.
4th term = 54 `=>` ar3 = 54
7th term = 1458 `=>` ar6 = 1458
Now, `(ar^6)/(ar^3) = 1458/54`
`=>` r3 = 27
`=>` r = 3
ar3 = 54
`=>` a × (3)3 = 54
`=> a = 54/27 = 2`
∴ G.P. = a, ar, ar2, ar3, ........
= 2, 2 × 3, 2 × (3)2, 54, ...........
= 2, 6, 18, 54, ............
APPEARS IN
संबंधित प्रश्न
Which term of the G.P.:
`-10, 5/sqrt(3), -5/6,....` is `-5/72`?
Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
The fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?
Find the sum of G.P. : 3, 6, 12, .........., 1536.
Q 7
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
