Find the 11th term in geometric sequence

Question

a₃ is24 and a₅ is 96

Answer 1

A geometric sequence has a common ratio r.

You are given a₃ = 24 and a₅ = 96

So, you can find r because:

a₅ / a₄ = r = 96 / a₄

a₄ / a₃ = r = a₄ / 24

multiply these together:

r*r = (96/a₄)*(a₄/24)

r*r = 4

r = 2 or -2 [note that 3 and 5 are odd term numbers, so r could be either ]

However, in either case, the 11th term is 6144.

Answer 2

with only 2 elements, it is difficult to be certain of the sequence, but a choice is to start with the number 6, and multiply by 2

 

in that case, the sequence will be:

a1  a2  a3  a4  a5   a6    a7    a8    a9     a10    a11

6    12  24  48  96  192  384  768  1536  3072  6144