Question

What is the next term in the multiplication or ,geometric , pattern that begins 13, 39, 117

Answer 1

Next term of the sequence is 351.

Explanation:

The given sequence is 13, 39, 117, A.In this sequence we have to find out the next term A of the sequence.

First we will understand whether the sequence is arithmetic or geometric sequence.

Sequence is in the form of 13, 3.(13), 3²(13).....

Therefore the sequence is a geometric sequence having common ratio r = Second term/first term = Third term/Second term

r = 3×13/13 = 3

Therefore nth term of the sequence
`T_(n)=ar^(n-1)`

`T_(n)=13.(3)^(n-1)`

Since we have to find fourth term A which will be

`T_(4)=A=13(3)^(4-1)=13(3)^(3)`

A = 13×27 = 351

Next term of the sequence is 351.