Question

Write a formula for the general term (the nth term) of the arithmetic sequence a1 = 200, d = -20. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.

Answer 1

a₂₀ = - 180

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + d(n - 1)

a₁ is the first term and d the common difference

given a₁ = 200 and d = - 20

substitute these values into the nth term formula

`a_(n)` = 200 - 20(n - 1) = 200 - 20n + 20 = - 20n + 220

substitute n = 20 into the formula to obtain a₂₀

a₂₀ = - 20(20) + 220 = - 400 + 220 = - 180