Question

2,6,10,14 and 102,96,90 are two ap which term of these ap will be equal​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{A.Ps are 2,6,10,14.......and}$

$\textsf{102,96,90....}$

$\underline{\textsf{To find:}}$

$\textsf{The term in which these two A.Ps are equal}$

$\underline{\textsf{Solution:}}$

$\textsf{Concept:}$

$\textsf{The n th term of the A.P a, a+d,.......is}$

$\boxed{\mathsf{t_n=a+(n-1)d}}$

$\textsf{For the A.P, 2,6,10,.....}$

$\textsf{n th term is}\;\mathsf{2+(n-1)4}$

$\textsf{For the A.P, 102,96,90,.....}$

$\textsf{n th term is}\;\mathsf{102+(n-1)(-6)}$

$\textsf{As per given condition,}$

$\mathsf{2+(n-1)4=102+(n-1)(-6)}$

$\mathsf{2+4n-4=102-6n+6}$

$\mathsf{4n-2=108-6n}$

$\mathsf{4n+6n=108+2}$

$\mathsf{10\,n=110}$

$\implies\boxed{\mathsf{n=11}}$

$\underline{\textsf{Answer:}}$

$\textsf{11 th term of both the A.Ps are equal}$

$\textbf{Find more:}$

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