Mathematics

Find the sum of terms of the A.P. : 4, 9, 14, ……, 89.

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Let there be n terms in the above series.

From above series,

a_n = 89, a = 4 and d = 5.

By formula,

⇒ a_n = a + (n - 1)d

⇒ 89 = 4 + 5(n - 1)

⇒ 85 = 5(n - 1)

⇒ 17 = n - 1

⇒ n = 18.

By formula,

Sum of A.P. = $\dfrac{n}{2}(a + a_n)$

Substituting values we get,

$= \dfrac{18}{2}(4 + 89) \\[1em] = 9 \times 93 \\[1em] = 837.$

Hence, sum of A.P. = 837.

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