Find the number of terms of the finite A.P. - | vedclass

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(C) The given $A.P.$ is $-1, -\frac{5}{6}, -\frac{2}{3}, \ldots, \frac{10}{3}$.Here,the first term $a = -1$.The common difference $d = -\frac{5}{6} -

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(C) The given $A.P.$ is $-1, -\frac{5}{6}, -\frac{2}{3}, \ldots, \frac{10}{3}$.Here,the first term $a = -1$.The common difference $d = -\frac{5}{6} - (-1) = -\frac{5}{6} + 1 = \frac{1}{6}$.The last term $a_n = \frac{10}{3}$.The formula for the $n^{th}$ term of an $A.P.$ is $a_n = a + (n - 1)d$.Substituting the values: $\frac{10}{3} = -1 + (n - 1)\frac{1}{6}$.Adding $1$ to both sides: $\frac{10}{3} + 1 = (n - 1)\frac{1}{6}$.$\frac{13}{3} = (n - 1)\frac{1}{6}$.Multiplying both sides by $6$: $13 	imes 2 = n - 1$.$26 = n - 1$.$n = 27$.Thus,the number of terms is $27$.

Find the number of terms of the finite $A.P.$ $-1, -\frac{5}{6}, -\frac{2}{3}, \ldots, \frac{10}{3}$.

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