Question

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

$0,-4,-8,-12,$

Answer 1

$0,-4,-8,-12$

$\Rightarrow$ Difference between second and first term $=-4-0=-4$

$\Rightarrow$ Difference between third and second term $=-8-(-4)=-8+4=-4$

$\Rightarrow$ Difference between fourth and third term $=-12-(-8)=-12+8=-4$

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

$\Rightarrow$ Common difference $=d=-4$

$\Rightarrow$ 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 $=4^{th}term+d=-12+(-4)=-16$

$\Rightarrow$ $6^{th}$ term $=5^{th}term+d=-16+(-4)=-20$

$\Rightarrow$ $7^{th}$ term $=6^{th}term+d=-20+(-4)=-24$

Hence $5^{th},6^{th}$ and $7^{th}$ terms are $-16,-20,-24$