Mathematics

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

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Let n be no. of terms,

∴ a_n = a + (n - 1)d

⇒ 700 = 34 + (n - 1)18

⇒ 700 = 34 + 18n - 18

⇒ 700 = 18n + 16

⇒ 700 - 16 = 18n

⇒ 18n = 684

⇒ n = 38.

$S = \dfrac{n}{2}(a + l) \\[1em] = \dfrac{38}{2} \times (34 + 700) \\[1em] = 19 \times 734 \\[1em] = 13946.$

Hence, no. of terms = 38 and sum = 13946.

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