Question

Find the nth term for 13 8 3 -2 -7 and the 100th term

Answer 1

see explanation

Explanation:

there is a common difference between consecutive terms in the sequence, that is

8 - 13 = 3 - 8 = - 2 - 3 = - 7 - (- 2) = - 5

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = - 5 , then

`a_(n)` = 13 - 5(n - 1) = 13 - 5n + 5 = 18 - 5n

then

a₁₀₀ = 18 - 5(100) = 18 - 500 = - 482