Question

What is the general term of the sequence `{10,-20,40,-80,....}`?

Answer 1

General term of given sequence is `10xx(-2)^(n-1)`

Explanation:

Here the ratio between a term and its preceding term is constant as `-20/10=40/-20=-80/40=-2`

Hence it a geometric sequence with first term as `10` and common ratio as `-2`.

The general term of a geometric sequence with first term as `a` and common ratio as `r` is `axxr^(n-1)`.

Hence, general term of given sequence is `10xx(-2)^(n-1)`