To Find: AP and its 30^th term (i.e. a₃₀=?)

Given: a₅=5 and a₁₃=–3

Formula Used: a_n = a + (n - 1)d

(Where a=a₁ is first term, a₂ is second term, a_n is nth term and d is common difference of given AP)

By using the above formula, we have

a₅ = 5 = a + (5 - 1)d , and a₁₃ = –3 = a + (13 - 1)d

a + 4d =5 and a + 12d = –3

on solving above 2 equation, we and a + 12d = –3get

a = 9 and d= (–1)

So a₃₀ = 9 + 29(–1) = –20

AP is (9,8,7,6,5,4……) and 30^th term = –20