Question

Find the number of terms in each of the following AP's
$7,13,19,....205$

• A. $20$ terms
  
• B. $28$ terms
  
• C. $34$ terms
  
• D. $40$ terms
  

Answer 1

The correct option is C $34$ terms

Clearly, the given Sequence is an AP with first term $a=7$ and common difference $d=13-7=6$.
Let $205$ be the $nth$ term of the given AP.
$\Rightarrow a_n=205$
$\Rightarrow a+(n-1)d=205$

$\Rightarrow 7+(n-1)\times 6=205$

$\Rightarrow (n-1)\times 6=198$
$\Rightarrow n=34$
Hence, there are $34$ terms in the given AP.