Mathematics

There are total 9 terms in an A.P. If the last term and the sum of all the terms are 28 and 144 respectively, then the first term is :
1
7
4
5

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We know that,

S_n = $\dfrac{n}{2}$ (a + l)

Given,

n = 9

l = 28

S_n = 144

⇒ S₉ = $\dfrac{9}{2}$ (a + 28)

⇒ 144 = $\dfrac{9}{2}$ (a + 28)

⇒ $\dfrac{144 \times 2}{9}$ = (a + 28)

⇒ 32 = (a + 28)

⇒ 32 - 28 = a

⇒ a = 4.

Hence, option 3 is the correct option.

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