Which term of the A.P. 20, 19 frac{1}{4}, 18 | vedclass

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Question

(A) For the given $A.P.$ $20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots$,the first term $a = 20$ and the common difference $d = 19 \frac{

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(A) For the given $A.P.$ $20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots$,the first term $a = 20$ and the common difference $d = 19 \frac{1}{4} - 20 = -\frac{3}{4}$.Suppose the $n^{th}$ term of the $A.P.$ is its first negative term,so $T_n Using the formula $T_n = a + (n - 1)d$,we have $20 + (n - 1)(-\frac{3}{4}) $20 $20 	imes \frac{4}{3} $\frac{80}{3} $26.66 + 1 $n > 27.66$.Since $n$ must be a natural number,the smallest integer greater than $27.66$ is $28$.Therefore,the $28^{th}$ term is the first negative term of the $A.P.$

Which term of the $A.P.$ $20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots$ is its first negative term (in $^{th}$)?

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