Q23 of 24 Page 115

In an A.P. the sum of first ten terms is 80 and the sum of next ten terms is 280. Find the A.P.

Let the first term of AP be ‘a’ and common difference be ‘d’.


We know, sum of ‘n’ terms of an AP is



Given,


Sum of first test ten terms, S10 = 80 ……[1]



⇒ 5(2a + 9d) = 80


⇒ 2a + 9d = 16 ……[2]


Also, sum of next ten terms = 280


⇒ S20 – S10 = 280


⇒ S20 – 80 = 280 [From 1]


⇒ S20 = 360



⇒ 2a + 19d = 36 ……[3]


On subtracting [2] from [3]


2a + 19d – 2a – 9d = 36 – 16


⇒ 10d = 20


⇒ d = 2


Putting d = 2 in [2]


⇒ 2a + 18 = 16


⇒ a = –1


Hence, AP is


–1, –1 + 2, –1 + 2(2), …


–1, 1, 3, …


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