Question

5th and 12th term of gp are 32 and 4096 then find nth term

Answer 1

Hi ,

Let a and r are first term and common ratio

of a G.P .

It's given that ,

5th term = 32

ar⁴ = 32 ----( 1 )

12th term = 4096

ar^11 = 4096 ---( 2 )

Do ( 2 ) ÷ ( 1 ) ,

( ar^11 )/ ( ar⁴ ) = 4096/32

r^7 = 128

r^7 = 2^7

r = 2 --( 3 )

substitute r = 2 in equation ( 1 ) , we get

ar⁴ = 32

a × 2⁴ = 32

a × 16 = 32

a = 32/16

a = 2

Therefore ,

nth term = an = ar^n-1

an = 2 × 2^n-1

= 2^1+n-1

= 2ⁿ

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!


Thanks