Question

Check whether given series is $APs$? If they form an $AP$, find the common difference $d$ and write three more terms.
$-1.2,-3.2,-5.2,-7.2,....$

Answer 1

The given series is $-1.2,-3.2,-5.2,-7.2,\cdots$.

$a_2-a_1=-3.2-\left(-1.2\right)$

$=-3.2+1.2$

$=-2$

$a_3-a_2=-5.2-\left(-3.2\right)$

$=-5.2+3.2$

$=-2$

$a_4-a_3=-7.2-\left(-5.2\right)$

$=-7.2+5.2$

$=-2$

This shows that the difference is same, so the given series is in A.P. with common difference $-2$. The next three terms are,

$a_5=-7.2+\left(-2\right)$

$=-7.2-2$

$=-9.2$

$a_6=-9.2+\left(-2\right)$

$=-9.2-2$

$=-11.2$

$a_7=-11.2+\left(-2\right)$

$=-11.2-2$

$=-13.2$