Question

Write an equation for the nth term of the arithmetic sequence then find a10. -2,5,12,19

Answer 1

see explanation

Explanation:

The nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 2 and d = a₂ - a₁ = 5 - (- 2) = 5 + 2 = 7 , then

`a_(n)` = - 2 + 7(n - 1) = - 2 + 7n - 7 = 7n - 9

Use this formula to find a₁₀

a₁₀ = 7(10) - 9 = 70 - 9 = 61