Question

Find the nth term of the progression − 5 − 3 − 1 + 1 + ...

Answer 1

d = −3 − (−5) = 2

d = −1 − (−3) = 2

d = 1 − (−1) = 2

Since the difference is constant, this is an Arithmetic Progression (AP) where the first term 𝑎 = −5 and the common difference 𝑑 = 2

a_n = a + (n − 1)d

Substitute the values a = −5 and d = 2 into the formula:

a_n = −5 + (n − 1)2

a_n = −5 + 2n − 2

a_n = 2n − 7