For the finite A.P. 3, 5, 7, ldots, 201,find | vedclass

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(D) The given sequence is an $A.P.$ with the first term $a = 3$ and common difference $d = 5 - 3 = 2$.Let there be $n$ terms in this $A.P.$ The last t

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$179$

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(D) The given sequence is an $A.P.$ with the first term $a = 3$ and common difference $d = 5 - 3 = 2$.Let there be $n$ terms in this $A.P.$ The last term $l = 201$.Using the formula $l = a + (n - 1)d$:$201 = 3 + (n - 1)2$$198 = (n - 1)2$$n - 1 = 99$$n = 100$.The $k^{th}$ term from the end is given by the formula $(n - k + 1)^{th}$ term from the beginning.Here,$k = 12$ and $n = 100$.So,the $12^{th}$ term from the end is the $(100 - 12 + 1)^{th} = 89^{th}$ term from the beginning.$a_{89} = a + (89 - 1)d$$a_{89} = 3 + 88 	imes 2$$a_{89} = 3 + 176 = 179$.

For the finite $A.P.$ $3, 5, 7, \ldots, 201$,find the $12^{th}$ term from the end.

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