Question

Use inductive reasoning to find the 10th term in the sequence 5, 8, 11, 14, ...

Answer 1

\[5,8,11,14\]
Difference is 3 in all of them so the formula for the n term is simply the first term times a multiple of 3:
\[ a_n=5+3n \;\;\;\;\; where \;\;n>=0.\]
so the first is when n=0, namely 5, so the 10th term is when n=9, namely:
\[5+3*9=5+27=32\]

Answer 2

Thanks so much! You've not only helped me with the answer, but with understaning this.

Answer 3

:)