Question

Is the following sequence an $AP$? If true, find the common difference $d$ and write three more terms.

$-1.2,-3.2,-5.2,-\mathrm{7.2...}$

Answer 1

$-1.2,-3.2,-5.2,-7.2$

$\Rightarrow$ Difference between second and first term $=-3.2-(-1.2)=-3.2+1.2=-2$

$\Rightarrow$ Difference between third and second term $=-5.2-(-3.2)=-5.2+3.2=-2$

$\Rightarrow$ Difference between fourth and third term $=-7.2-(-5.2)=-7.2+5.2=-2$

$\Rightarrow$ Since, difference is same, it is an $A.P$

$\Rightarrow$ Common difference $=d=-2$

$\Rightarrow$ We have to find next three terms. We are given $4$ terms.

$\Rightarrow$ We have to find $5^{th},6^{th}$ and $7^{th}$ terms.

$\Rightarrow$ $5^{th}$ term $=4^{th}term+d=-72+(-2)=-9.2$

$\Rightarrow$ $6^{th}$ term $=5^{th}term+d=-9.2+(-2)=-11.2$

$\Rightarrow$ $7^{th}$ term $=6^{th}term+d=-11.2+(-2)=-13.2$

Hence $5^{th},6^{th}$ and $7^{th}$ terms are $-9.2,-11.2,-13.2$