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Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

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Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
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Solution:

Given d = 7,
22nd term = 149 , 
⇒ a+21d = 149
⇒a+21(7) = 149
⇒a+147 = 149
⇒a=149-147=2
Sn = (n/2)(2a+(n-1)d)
S₂₂ = (22/2)(2×2+(22-1)7)
S₂₂ = 11(4+21(7))
S₂₂ = 11(4+147)
S₂₂ = 11(151)
S₂₂ = 1661.

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