Question

find the first term and the common ratio of the GP whose seventh and 12th terms are respectively 192 and 6144​

Answer 1

Step-by-step explanation:

If a₁ is the first term, a_{n}a

n

is the nth term and r is the common ratio of the given G.P. series then

a_{n}a

n

=a₁rⁿ⁻¹

a₈=a₁×(2)⁸⁻¹=192

or, a₁×2⁷=192

or, a₁=192/2⁷

or, a₁=2⁶×3/2⁷

or, a₁=3/2

∴, a₁₂=a₁r¹²⁻¹

=3/2×(2)¹¹

=3×(2)¹⁰

=3×1024

=3072

Answer 2

Step-by-step explanation:

Let first term of GP be a

Let common ratio be r

a7=192

a.r^6=192

a = 192/r^6

a12 =6144

a.r^11=6144

192.r^11 = 6144

r^6

192.r^5= 6144

r^5= 32

r= 2

a= 192/64= 3

1st term is 3

common ratio is 2