Question

2.8, 3.4, 4.0, 4.6, . . . Write an equation for the nth term of the arithmetic sequence. Then find a50.

Answer 1

a_n = 2.2 + 0.6 n

a_50 = 32.2

Explanation:

What's the common difference of this series?

`a_1 = 2.8`

`a_2 = 3.4`

Common difference =
`a_2 - a_1 = 3.4 - 2.8 = 0.6`.

Expression for the nth term:

`a_n = a_1 + (n - 1) \cdot\text{Common Difference} \\\phantom{a_n } = 2.8 + 0.6 \; (n-1) \\\phantom{a_n} = 2.8 + 0.6 \; n - 0.6\\\phantom{a_n} = 2.2 + 0.6\; n`

n = 50 for the fiftieth term. Therefore

`a_(50) = 2.2 + 0.6 * 50 = 32.2`.