Question

Find the 14th term of the following geometric sequence.
4, 8, 16, 32, ...

Answer 1

65536

Explanation:

multiply each term by 2 until you get to the 14th term. the 14th term is 65536

Answer 2

32768

Explanation:

`an = (a1)(r^(n-1) )\\\\`

where an stands for the number in the series,

a1 is the first number in the series

and n is the number or the order in which the number in the series we are looking at. r is the ratio.

in this we case we are looking for the 14th number, where n = 14, the first number is 4 and r is the ratio they increase by a factor of 2. so r = 2.

Substituting all of these back into the equations would give us:

`a14 = 4(2^(13) )`

This will give us the answer.