Question

What is the 50th term of the sequence that begins -4, 2, 8, 14....?

Answer 1

`a_(50)=290`

Explanation:

Notice that we are in the presence of an arithmetic sequence (there is a common difference of 6 between a term and the next). So thisis an arithmetic sequence with first term
`a_1=-4`. and common difference "d" = 6.

Recall now the formula for the nth term (
`a_n`) of an arithmetic sequence:

`a_n=a_1+(n-1)\,d`

Then, using our values in the formula, we get:

`a_n=a_1+(n-1)\,d\\a_(50)=-4+(50-1)\,6\\a_(50)=-4+(49)\,6\\a_(50)=290`