Question

Find the of 7th and 9th elements of G.p
4,1,1/4,1/6...
a=4
r=T2/T1=1/4
tr=ar(n-1)​

Answer 1

Answer: a=4 r=1/4

a7 = ar^(7-1)

a7 = 4 x (1/4)^6

a7 = 4 x 1/4096

a7 = 1/1024

a9 = ar^(9-1)

a9 = 4x 1/4^8

a9 = 4 x 1/65536

a9 = 1/16384

Step-by-step explanation:

Answer 2

Answer :-

a_7 = 1/4^5

a_9 = 1/4^7

Solution :-

Given :-

4, 1, 1/4, 1/16, .... are in GP

First term of GP ( a ) = 4

Common ratio ( r ) = a_n / a_(n - 1) = a_2 / a_1 = 1/4

Using nth term of GP formula

a_n = ar^( n - 1 )

Seventh term of GP = a_7 = ar^( 7 - 1 )

= ar^6

= 4 * ( 1/4 )^6

= 4 * 1/4^6

= 1/4^5

Ninth term of GP = a_9 = ar^( 9 - 1 )

= ar^8

= 4 * ( 1/4 )^8

= 4 * 1/4^8

= 1/4^7

Therefore seventh term is 1/4^5 and ninth term is 1/4^7.