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Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Updated On: Jan 13, 2026
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Solution and Explanation
\(d = 7\), \(a_{22} = 149\), \(S_{22 }=?\)
The formula for the nth term of an arithmetic sequence is \(a_n = a + (n − 1)d\).
Substituting the known values for the 22nd term: \(a_{22} = a + (22 − 1)d\).
Plugging in the given values: \(149 = a + 21 × 7\).
Simplifying: \(149 = a + 147\).
Solving for the first term, a: \(a = 2\).
The formula for the sum of an arithmetic series is \(S_n = \frac n2[a + a_n]\).
Calculating the sum of the first 22 terms: \(S_{22} = \frac {22}{2 }[2 + 149]\).
Simplifying the expression: \(S_{22}= 11 \times 151\).
The final sum is: \(S_{22}= 1661\).
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