Question

The 5th term of a g.p. is 1/3 and 9th term is 16/243 find its 4th term

Answer 1

Answer:

1/2

Step-by-step explanation:

Let a be the first term and r be the common ratio.  Then:

5th term = a r^4 = 1/3

9th term = a r^8 = 16/243

So r^4 = ( a r^8 ) / ( a r^4 ) = (16/243) / (1/3) = 16 / 81 = ( 2 / 3 )^4

So r = 2 / 3 (can we assume that r is positive?)

and a = ( 1/3) / (r^4) = (1/3) / (2/3)^4 = 3^3 / 2^4

Finally,

4th term = a r^3 = (3^3 / 2^4) × ( 2 / 3 )³ = 1/2

Answer 2

Answer:

1/2

Step-by-step explanation:

Let a be the first term and r be the common ratio.

$5th term = a r^4 = 1/39th term = a r^8 = 16/243r^4 = ( a r^8 ) / ( a r^4 ) = (16/243) / (1/3) = 16 / 81 = ( 2 / 3 )^4 r = 2 / 3 a = ( 1/3) / (r^4) = (1/3) / (2/3)^4 = 3^3 / 2^44th term = a r^3 = (3^3 / 2^4) × ( 2 / 3 )³ = 1/2$