Find the number of terms in the following AP: | vedclass

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(C) Given $AP$ is $18, 15 \frac{1}{2}, 13, \ldots, -47$.Here,the first term $a = 18$.The common difference $d = a_2 - a_1 = 15 \frac{1}{2} - 18 = \fra

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(C) Given $AP$ is $18, 15 \frac{1}{2}, 13, \ldots, -47$.Here,the first term $a = 18$.The common difference $d = a_2 - a_1 = 15 \frac{1}{2} - 18 = \frac{31}{2} - 18 = \frac{31 - 36}{2} = -\frac{5}{2}$.Let the number of terms in this $AP$ be $n$. The $n^{th}$ term is $a_n = -47$.Using the formula $a_n = a + (n - 1)d$:$-47 = 18 + (n - 1)\left(-\frac{5}{2}ight)$Subtract $18$ from both sides:$-47 - 18 = (n - 1)\left(-\frac{5}{2}ight)$$-65 = (n - 1)\left(-\frac{5}{2}ight)$Multiply both sides by $-\frac{2}{5}$:$n - 1 = -65 	imes \left(-\frac{2}{5}ight)$$n - 1 = 13 	imes 2$$n - 1 = 26$$n = 27$.Thus,the given $AP$ has $27$ terms.

Find the number of terms in the following $AP$: $18, 15 \frac{1}{2}, 13, \ldots, -47$.

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