For the finite A.P. 3, 8, 13, ldots, 253, fin | vedclass

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Question

(B) For the given $A.P.,$ the first term $a = 3$ and the common difference $d = 8 - 3 = 5$.If $253$ is the $n^{th}$ term of the $A.P.,$ then$253 = 3 +

Vedclass · Accepted Answer

$158$

Vedclass · Answer

(B) For the given $A.P.,$ the first term $a = 3$ and the common difference $d = 8 - 3 = 5$.If $253$ is the $n^{th}$ term of the $A.P.,$ then$253 = 3 + (n - 1)5$$250 = 5(n - 1)$$50 = n - 1$$n = 51$Thus,there are $51$ terms in the given finite $A.P.$The $20^{th}$ term from the end is equivalent to the $(51 - 20 + 1)^{th} = 32^{nd}$ term from the beginning.$T_{32} = a + (32 - 1)d$$T_{32} = 3 + 31(5)$$T_{32} = 3 + 155$$T_{32} = 158$Hence,the $20^{th}$ term from the end of the given $A.P.$ is $158.$

For the finite $A.P.$ $3, 8, 13, \ldots, 253,$ find the $20^{th}$ term from the end.

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