Find the sum of the first 51 terms of an AP w | vedclass

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(D) Given that,the second term $a_{2} = 14$ and the third term $a_{3} = 18$.The common difference $d$ is given by $d = a_{3} - a_{2} = 18 - 14 = 4$.Si

Vedclass · Accepted Answer

$5610$

Vedclass · Answer

(D) Given that,the second term $a_{2} = 14$ and the third term $a_{3} = 18$.The common difference $d$ is given by $d = a_{3} - a_{2} = 18 - 14 = 4$.Since $a_{2} = a + d$,we have $14 = a + 4$,which gives the first term $a = 10$.The sum of the first $n$ terms of an $AP$ is given by $S_{n} = \frac{n}{2}[2a + (n - 1)d]$.For $n = 51$,$S_{51} = \frac{51}{2}[2(10) + (51 - 1)4]$.$S_{51} = \frac{51}{2}[20 + (50)(4)]$.$S_{51} = \frac{51}{2}[20 + 200] = \frac{51}{2}(220)$.$S_{51} = 51 	imes 110 = 5610$.

Find the sum of the first $51$ terms of an $AP$ whose second and third terms are $14$ and $18$ respectively.

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