Question

How do you write the first five terms of the geometric sequence a1 = 8; r = 5?

Answer 1

The first five terms of the given geometric sequence are `8,40,200,1000,5000`.

Explanation:

The general term for a geometric sequence is

`a_n=a_1r^(n-1)`

Where `a_n` is the nth term, `a_1` is first term `r` is the common ratio and `n` is the position or number of the term.

Here `a_1=8` and `r=5`

Put `n=2` `implies a_2=8*5^(2-1)=8*5=40`
Put `n=3` `implies a_3=8*5^(3-1)=8*5^2=8*25=200`
Put `n=4` `implies a_4=8*5^(4-1)=8*5^3=8*125=1000`
Put `n=5` `implies a_5=8*5^(5-1)=8*5^4=8*625=5000`

Hence, the first five terms of the given geometric sequence are `8,40,200,1000,5000`.