Question

The arithmetic sequence a_n is defined below. Find the first five terms of the sequence. a_1 = −6, d=8. Which of the following represents the correct first five terms of the sequence?

a) -6, 2, 10, 18, 26
b) -6, 8, 16, 24, 32
c) -6, 14, 22, 30, 38
d) -6, 0, 8, 16, 24

Answer 1

Using the arithmetic sequence formula, the first five terms of the sequence with a_1 = -6 and d = 8 are -6, 2, 10, 18, 26.

Step-by-step explanation:

To find the first five terms of an arithmetic sequence, we use the formula, where a_n is the nth term, a_1 is the first term, and d is the common difference between the terms.

Given a_1 = -6 and d = 8, we can calculate the first five terms:

1. a_2 = a_1 + d = -6 + 8 = 2
2. a_3 = a_2 + d = 2 + 8 = 10
3. a_4 = a_3 + d = 10 + 8 = 18
4. a_5 = a_4 + d = 18 + 8 = 26

Therefore, the correct first five terms of the sequence are -6, 2, 10, 18, 26.