Question

which term of the ap -67,-62,-57 ..... is the first positive term​

Answer 1

$\red{\underline{\underline{Answer:}}}$

$\sf{15^{th} \ term \ of \ A.P. \ is \ positive \ term.}$

$\orange{Given:}$

$\sf{The \ given \ A.P. \ is }$

$\sf{-67,-62,-57,…}$

$\sf\pink{To \ find:}$

$\sf{First \ positive \ term \ of \ A.P.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{t1= -67}$

$\sf{t2= -62}$

$\sf{Common \ difference \ (d)=t2-t1}$

$\sf{t2-t1= -62-(-67)=5}$

$\sf{Multiple \ of \ 5 \ more \ than \ 67 \ is \ 70}$

$\sf{\therefore{n=\frac{70}{5}+1}}$

$\sf{n=14+1=15}$

$\sf\blue{\underline{\underline{Verification:}}}$

$\sf{tn=a+(n-1)d... formula}$

$\sf{t15=-67+(15-1)5}$

$\sf{t15=-67+14(5)}$

$\sf{t15=-67+70}$

$\sf{\therefore{t15=3}}$

$\sf\purple{\tt{\therefore{15^{th} \ term \ of \ A.P. \ is \ positive \ term.}}}$

Answer 2

$\huge\underline\mathfrak\red{Answer:}$

$\rm\pink{ {15}^{th} \ term \ is \ the \ first \ positive \ term \ of \ the \ AP}$

_________________________________________

$\sf\large\underline\green{Given:}$

$\rm{AP \ is \ -67, \ -62, \ -57 ......}$

_________________________________________

$\sf\large\underline\green{To \ Find:}$

$\rm{First \ positive \ term \ of \ the \ AP}$

_________________________________________

$\huge\underline\mathfrak\blue{Solution:}$

$\rm{First \ term \ of \ the \ AP :}$

$\rm{t(1)= -67}$

$\rm{Second \ term \ of \ the \ AP :}$.

$\rm{t(1)= -62}$

$\rm{Difference \ between \ two \ successive \ terms }$

$d = t2- t1$

$d = - 62- ( - 67) = 5$

$\rm{now , \ multiple \ of \ 5 \ more \ than \ 67 \ is \ 70}$

$n = ( \frac{70}{5} ) + 1$

$n = 14 + 1$

$n = 15$

$\rm\pink{ {15}^{th} \ term \ is \ the \ first \ positive \ term \ of \ the \ AP}$

_________________________________________

$\rm{hope \ it \ helps }$ :))