Question

Before using the Gizmo, consider an arithmetic sequence with a first term (a1) of 4 and a common difference (d) of 3.

Challenge: What are the first five terms of the sequence (from lowest to highest)?

Answer 1

4, 7, 10, 13 and 16

Explanation:

The nth term of an arithmetic sequence is expressed as
`Tn = a+(n-1)d`.

a is the first term of the sequence

d is the common difference

n is the number of terms

Given the first term a = 4 and common difference d = 3, we can calculate the first five terms of the sequence using the formula.

If n = 2

`T_2 = 4+(2-1)*3\\T_2 = 4+(1)*3\\T_2 = 4+3\\T_2 = 7\\\\when \ n = 3;\\T_3 = 4+(3-1)*3\\T_3 = 4+(2)*3\\T_3 = 4+6\\T_3 = 10\\\\when\ n = 4\\T_4 = 4+(4-1)*3\\T_4 = 4+(3)*3\\T_4 = 4+9\\T_4 = 13\\\\when\ n = 5\\T_5 = 4+(5-1)*3\\T_5 = 4+(4)*3\\T_5 = 4+12\\T_5 = 16\\`

The first five terms of the sequence from lowest to highest are 4, 7, 10, 13 and 16