Question

If the 5th term of a G.P. is 16 and 10" term is 1/2, then 15" term is:​

Answer 1

Step-by-step explanation:

SOLUTION:-

As we know in G.P , the n th term is ar^n-1

so the 5th term is 16 and 10th term is 1/2

ar^5-1=16

=>ar^4=16-------(1)

then ar^10-1=1/2

=>ar^9=1/2-------(2)

By comparing both we get,

ar^4/ar^9=16/1/2

=>1/r^5=32=2^5

=>1/r=2

=>r=1/2

By putting the value of r in equation 1 we get,

a=16×32=512

so 15th term is:

ar^15-1=ar^14=512(1/2)^14

=8388608