Class 10

Math

All topics

Arithmetic Progressions

The $7$th term of an AP is $−4$ and its $13$th term is $−16$. Find the AP.

Let us say $a$ be the first term and $d$ be the common difference of an AP.

$a_{n}=a+(n−1)d$

$a_{7}=a+(7−1)d$

$=a+6d=−4$ ...........$(1)$

And $a_{13}=a+12d=−16$ ........$(2)$

Subtracting equation $(1)$ from $(2)$, we get

$6d=−16−(−4)=−12$

From $(1)$, $a+6d=−4$

$a+(−12)=−4$

$a=−4+12=8$

$a=8,d=−2$

AP will be $8,6,4,2,0,...$.