Find the sum of first 22 terms of an AP in wh | vedclass

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(C) Given: Common difference $d = 7$,number of terms $n = 22$,and the $22^{nd}$ term $a_{22} = 149$.We know the formula for the $n^{th}$ term of an $A

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$1661$

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(C) Given: Common difference $d = 7$,number of terms $n = 22$,and the $22^{nd}$ term $a_{22} = 149$.We know the formula for the $n^{th}$ term of an $AP$ is $a_n = a + (n - 1)d$.Substituting the values: $149 = a + (22 - 1) 	imes 7$.$149 = a + 21 	imes 7$.$149 = a + 147$.$a = 149 - 147 = 2$.Now,the formula for the sum of the first $n$ terms is $S_n = \frac{n}{2}(a + a_n)$.Substituting the values: $S_{22} = \frac{22}{2}(2 + 149)$.$S_{22} = 11 	imes 151$.$S_{22} = 1661$.

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

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