If the sum of it terms of an A.P. is 2$\mathbf{n}^{2}$ + 5n, then its nth term is
A. 4n – 3 B. 3n – 4 C. 4n + 3 D. 3n + 4 Answer: Option CShow Answer
Solution(By Apex Team)
Let a be the first term and d be the common difference of an A.P. and
$\begin{aligned}S_n&=2n^2+5n\\
\therefore S_1&=2(1)^2+5\times1\\
&\quad=2+5\\
&\quad=7\\
\therefore S_2&=2(2)^2+5\times2\\
&\quad=8+10\\
&\quad=18\\
\therefore\text{ First term }\left(a_1\right)&=7\text{ and }\\
\text{ Second term }a_2&=S_2-S_1\\
&\quad=18-7\\
&\quad=11\\
\therefore d&=a_2-d_1\\
&=11-7\\
&=4\\
\text{ Now }a_n&=a+(n-1)d\\
&\quad=7+(n-1)4\\
&\quad=7+4n-4\\
&=4n+3\end{aligned}$
Related Questions On Progressions
How many terms are there in 20, 25, 30 . . . . . . 140?
A. 22B. 25
C. 23
D. 24
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5B. 6
C. 4
D. 3
Find the 15th term of the sequence 20, 15, 10 . . .
A. -45B. -55
C. -50
D. 0
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600B. 765
C. 640
D. 680
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