Question

the first and the last term of AP are 17 and 350 respectively . if the common difference is 9 how many terms are there and what is the sum​

Answer 1

Please find the attachment

Answer 2

Step-by-step explanation:

AnswEr:

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

$\rule{150}2$

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

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

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

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

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

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

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

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

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

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

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

$\rule{150}2$

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

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

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

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

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

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

$\rule{150}2$