For an A.P. if $\mathbf{a}_{\mathbf{2 5}}-\mathbf{a _ { 2 0 }}$ = 45, then d equals to:
A. 9 B. -9 C. 18 D. 23 Answer: Option AShow Answer
Solution(By Apex Team)
$\begin{array}{l}a_n=a+(n-1)\times d\\
\Rightarrow a_{25}=a+24d\\
\text{ and }a_{20}=a+19d\\
a_{25}-a_{20}=45\\
\Rightarrow a+24d-a-19d=45\\
\Rightarrow5d=45\\
\Rightarrow d=9\end{array}$
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The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
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D. 680
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