Question

Check if given series is $APs$? If they form an $AP$, find the common difference $d$ and write three more terms.
$-10,-6,-2,2,...$

Answer 1

The given series is $-10,-6,-2,2,\cdots$.

$a_2-a_1=-6-\left(-10\right)$

$=-6+10$

$=4$

$a_3-a_2=-2-\left(-6\right)$

$=-2+6$

$=4$

$a_4-a_3=2-\left(-2\right)$

$=2+2$

$=4$

This shows that the difference is same, so the given series is in A.P. with common difference $4$. The next three terms are,

$a_5=2+4$

$=6$

$a_6=6+4$

$=10$

$a_7=10+4$

$=14$