Question

8. If in an A.P. , a10 = 35 and a45 = 140 , find the common difference.​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{In an A.P,}$

$\mathsf{a_{10}=35\;\;and\;\;a_{45}=140}$

$\underline{\textbf{To find:}}$

$\textsf{Common difference}$

$\underline{\textbf{Solution:}}$

$\mathsf{a_{10}=35\;\implies\;a+9d=35------(1)}$

$\mathsf{a_{45}=140\;\implies\;a+44d=140------(2)}$

$\mathsf{(1)-(2)\;\implies\;-35d=-105}$

$\implies\mathsf{d=\dfrac{-105}{-35}}$

$\implies\boxed{\bf\,d=3}$

$\underline{\textbf{Answer:}}$

$\textbf{Common difference is 3}$

$\underline{\textbf{Formula used:}}$

$\boxed{\begin{minipage}{8cm} \\\textsf{The n th term of the A.P, a, a+d, a+2d, . . . . .is}\\\\\mathsf{a_n=a+(n-1)d}\\ \end{minipage}}$