Find whether 55 is a term of the AP: 7, 10, 1 | vedclass

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(C) Let the first term be $a$, the common difference be $d$, and the number of terms be $n$ for the given $AP$.Given $AP$ is $7, 10, 13, \dots$Here, $

Vedclass · Accepted Answer

$17$

Vedclass · Answer

(C) Let the first term be $a$, the common difference be $d$, and the number of terms be $n$ for the given $AP$.Given $AP$ is $7, 10, 13, \dots$Here, $a = 7$ and $d = 10 - 7 = 3$.Let the $n^{th}$ term $T_n = 55$.The formula for the $n^{th}$ term of an $AP$ is $T_n = a + (n - 1)d$.Substituting the values, we get $55 = 7 + (n - 1) 	imes 3$.$55 - 7 = (n - 1) 	imes 3$.$48 = (n - 1) 	imes 3$.$n - 1 = 48 / 3 = 16$.$n = 16 + 1 = 17$.Since $n$ is a positive integer, $55$ is the $17^{th}$ term of the given $AP$.

Find whether $55$ is a term of the $AP: 7, 10, 13, \dots$ or not. If yes, find which term it is. (in $^{th}$)

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