Which term of the A.P. , 53, 48, 43, ldots is | vedclass

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(B) Given $A.P.$ is $53, 48, 43, \ldots$The first term $(a) = 53$ and the common difference $(d) = 48 - 53 = -5$.Let the $n^{th}$ term of the $A.P.$ b

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) Given $A.P.$ is $53, 48, 43, \ldots$The first term $(a) = 53$ and the common difference $(d) = 48 - 53 = -5$.Let the $n^{th}$ term of the $A.P.$ be the first negative term.Therefore,$T_n Using the formula for the $n^{th}$ term of an $A.P.$,$T_n = a + (n - 1)d$.Substituting the values,we get:$53 + (n - 1)(-5) $53 - 5n + 5 $58 - 5n $5n > 58$$n > 11.6$Since $n$ must be a positive integer,the smallest integer greater than $11.6$ is $12$.Thus,the $12^{th}$ term is the first negative term.Verification: $T_{12} = 53 + (12 - 1)(-5) = 53 + 11(-5) = 53 - 55 = -2$,which is less than $0$.

Which term of the $A.P. \, 53, 48, 43, \ldots$ is the first negative term?

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