The 5th and 13th terms of an AP are 5 and –3 respectively. Find the

1.	The 5th and 13th terms of an AP are 5 and –3 respectively. Find the AP and its 30th term.
Answer» 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, an is n^th 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 = –3 get a = 9 and d= (–1) So a₃₀ = 9 + 29(–1) = –20 AP is (9,8,7,6,5,4……) and 30^th term = –20

The 5th and 13th terms of an AP are 5 and –3 respectively. Find the AP and its 30th term.

Answer»

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, an is n^th 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 = –3 get

a = 9 and d= (–1)

So a₃₀ = 9 + 29(–1) = –20

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