We are told that the first term of a sequence is a_1= - 6 and that every term is 8 more than the one before. We need to find the value of the 101^(st) term. To begin, let's write down the first few terms of this sequence.
- 6+8 ⟶14+8 ⟶22+8 ⟶30+8 ⟶...
We see that the difference between any two consecutive terms is 8. Therefore, the given sequence is an arithmetic sequence. Recall that explicit equations for the nth term of an arithmetic sequence follow a certain format.
a_n= a_1+( n-1) d
In this form, a_1 is the first term in the sequence, d is the common difference, and n is the position of the desired term in the sequence. We are given that a_1= - 6 and d= 8, so we can substitute these values to write the equation.
a_n= - 6+( n-1) 8
Let's also simplify this equation.
