Question

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

$-10,-6,-2,2,$

Answer 1

$-10,-6,-2,2$

$\Rightarrow$ Difference between second and first term $=-6-(-10)=-6+10=4$

$\Rightarrow$ Difference between third and second term $=-2-(-6)=-2+6=4$

$\Rightarrow$ Difference between fourth and third term $=2-(-2)=2+2=4$

$\Rightarrow$ 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 $=4^{th}term+d=2+4=6$

$\Rightarrow$ $6^{th}$ term $=5^{th}term+d=6+4=10$

$\Rightarrow$ $7^{th}$ term $=6^{th}term+d=10+4=14$

Hence $5^{th},6^{th}$ and $7^{th}$ terms are $6,1014$