Question

Check if the series is an $AP.$ Find the common difference $d$. Also, find the next three terms.
$-10,-6,-2,\mathrm{2.....}$.

• A. It is an $AP$ and $d=4$, other terms $6,10,14$
  
• B. It is an $AP$ and $d=\frac{3}{5}$, other terms $5,10,15$
• C. It is not an $AP$, other terms $3,4,5$
  
• D. None of these
  

Answer 1

The correct option is A It is an $AP$ and $d=4$, other terms $6,10,14$

Given series is $-10,-6,-2,2,.......$

Clearly, the given sequence is an AP with first term $a=-10$ and common difference $d=-6-(-10)=4$
$n^{th}$ term $=a_n=a+(n-1)d$
$\Rightarrow a_5=a+4d=-10+4\times 4=6$
$\Rightarrow a_6=a+5d=-10+5\times 4=10$
$\Rightarrow a_7=a+6d=-10+6\times 4=14$