Question

The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?​

Answer 1

AnswEr:

$\frak{Given}\begin{cases} \sf{First\:Term\:(a)\:=\:17}\\ \sf{Last\:Term\:(L)\;=\; 350} \\ \sf{Common\: Difference\:(d)\:=\; 9}\end{cases}$

$\rule{150}2$

$\:\:\:\:\;\:\;\footnotesize\bold{\underline{\underline{\sf{\red{Formula\:For\:the\: Last\:Term\:is \:-}}}}}$

$\dag\;\:\large{\underline{\boxed{\sf{\purple{l\:=\; a + (n -1)d}}}}}$

$\large\bold{\underline{\sf{Putting\:Values-}}}$

$:\implies\sf \: 350 = 17 + (n -1)9$

$:\implies\sf \: 350 - 17 = (n - 1) 9$

$:\implies\sf \:333 = (n -1)9$

$:\implies\sf \:\cancel\dfrac{333}{9} = (n -1)$

$:\implies\sf \: (n -1) = 37$

$:\implies\sf \: n = 37 + 1$

$:\implies\large\boxed{\sf{\purple{n\:=\;38}}}$

$\small\bold{\underline{\sf{\red{Therefore\:Given\:AP\: Contains\: 38\:Terms.}}}}$

$\rule{150}2$

$\large\bold{\underline{\sf{Now\: Finding\: Sum -}}}$

$:\implies\sf \: S_{n} = \dfrac{n}{2} (a +l)$

$:\implies\sf \: S_{38} = \dfrac{38}{2}(17 + 350)$

$:\implies\sf \: 19 \times 367$

$:\implies\large\boxed{\sf{\purple{6973}}}$

$\small\bold{\underline{\sf{\red{Sum \:of \: the \:Terms\: of \: the \: Given\: AP\; is \: 6973.}}}}$

$\rule{150}2$

Answer 2

Tn=a+(n-1)d

350=17+(n-1)9

333=(n-1)9

n-1=37

N=38

Sum of all terms

Sn=n/2{a+l}

Sn=38/2{17+350}

Sn=19*367

Sn=6973