Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1. an = 7n2 − 5n − 6 , ,

Answer 1

To find the first three terms of the sequence defined by the formula $a_n=7n^2-5n-6$, we will substitute values of $n$ starting from 1.

1. For $n=1$: $$a_1=7(1{)}^2-5(1)-6=7(1)-5-6=7-5-6=-4$$

2. For $n=2$: $$a_2=7(2{)}^2-5(2)-6=7(4)-10-6=28-10-6=12$$

3. For $n=3$: $$a_3=7(3{)}^2-5(3)-6=7(9)-15-6=63-15-6=42$$

Putting it all together, the first three terms of the sequence are: $$a_1=-4,a_2=12,a_3=42$$

Therefore, the first three terms are $-4$, $12$, and $42$.