Question

the sum of arithematic series with 15 terms is 180.then the 8th term is.?​

Answer 1

$\blue{\underline{\underline {\huge{\mathfrak {\pink{Answer:-}}}}}}$

$\mathtt{the \: formula \: for \: the \: sum \: of \: an \: arithmetic}\\ \mathtt{ series \: is : }$

${\green {\boxed{ \mathtt{S = ( \frac{n}{2} )(1st + last)}}}}$

$\underline {\underline \mathtt \purple{Step \: by \: Step \: Explanation:-}}$

${ \underline { \underline\mathtt \red{given:-}}}$

$\mathtt{where \: n = the\:number \: of \: the \: term = 15} \\ \mathtt{ 1st = 1st \: term = x} \\ \mathtt{last = last \: term = x +( n - 1)(d)}$

${\underline {\underline\mathtt \orange{To \: find:-}}}$

$\mathtt{8th \: term \: of \: the \: series}$

$\mathtt\implies 18 = \frac{15}{2}(x + x + 14d) \\ \mathtt{\implies {18= \frac{15}{2}(2 x + 14d) }} \\ \mathtt{\implies { \frac{360}{15} = 2x + 14d}} \\ \mathtt{\implies {24 = 2x + 14d}} \\ \fbox {\boxed{\mathtt{\implies {12 = x + 7d}}}}$

$\mathtt{8th \: term = x + (8 - 1)d }\\ \mathtt{8th \: term = x + 7d}$

$\mathtt{As \: you \: can \: see \: the \: simplyfy \: the \: sum } \\ \mathtt{ of \: the \: series \: gave \: us \: that \: x + 7d \: was \: 12} \\ \boxed {\mathtt \blue{\therefore \: the \: 8th \: term \: is \: 12}}$