Question

An arithmetic sequence begins `1+a, 1+2a, 1+3a`. If the fifth term is `16`, what is the value of `a`?

Answer 1

See explanation.

Explanation:

From the given information we know, that:

`a_1=1+a`

`a_2=1+2a`

So we can calculate that the difference of the sequence is `d=a`.

Now we can calculate the value of `a` using the information that `a_5=16`

`a_5=a_1+4*d=(a+1)+4a=5a+1`

`5a+1=16 => 5a=15 => a=3`

Answer: The value of `a` is `a=3`