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Mathematics

Find the sum of first 22 terms of an A.P. in which d = 7 and a22 is 149.

AP GP

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Answer

Given, d = 7 and a22 = 149.

By formula, an = a + (n - 1)d

⇒ 149 = a + (22 - 1)7
⇒ 149 = a + 21(7)
⇒ 149 = a + 147
⇒ a = 149 - 147
⇒ a = 2.

By formula Sn = n2[2a+(n−1)d]\dfrac{n}{2}[2a + (n - 1)d]

⇒ Sn = 222[2×2+(22−1)7]\dfrac{22}{2}[2 \times 2 + (22 - 1)7]
⇒ Sn = 11[4 + 147]
⇒ Sn = 11 × 151
⇒ Sn = 1661.

Hence, the sum of first 22 terms of the A.P. is 1661.

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