Question

The first term of Ap is 5 last term is 45 and sum is 400 Find the numbers of terms and common difference ​

Answer 1

$\huge\boxed{\mathbb\red{GIVEN}}$

$\textbf{First\:term\:or\:a\:=\:5}$

$\textbf{Last\:Term\:or\:L\:=\:45}$

$\textbf{Sum\:=\:400}$

$\huge\boxed{\mathbb\pink{TO\:CALCULATE}}$

$\odot\textbf{Number\:of\:terms}$

$\odot\textbf{Common\:Difference\:or\:d}$

$\huge\boxed{\mathfrak\pink{Answer}}$

$\textsf{Sum= \dfrac{n}{2}(a+l) }$

$\textsf{where n is number of terms and a is first term}$

$\textsf{and l is the last term}$

$\textsf{ 400=\dfrac{n}{2}\:\times\:50 }$

$\textsf{n= \dfrac{400\:\times\:2}{50} }$

$\textsf{n=16}$

$\textsf{l=a+(n-1)d}$

$\textsf{ 45=5+(16-1)d }$

$\textsf{40=15d}$

$\textsf{ d=\dfrac{40}{15} }$

$\textsf{ d=\dfrac{8}{3} }$

$\huge\boxed{\mathcal\green{Note}}$

$\huge\boxed{\textsf{Formula Used}}$

$\odot\textsf{ Sum=\dfrac{n}{2}\:\times\:(a+l) }$

$\odot\textsf{ Last\:Term=a+(n-1)\:\times\:d }$

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Answer 2

Answer:

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