ssccglapex

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

A. 5 B. 6 C. 7 D. 8 Answer: Option B
Show Answer

Solution(By Apex Team)

First term of an A.P. (a) = 1 Last term (l) = 11 and sum of its terms = 36 Let n be the number of terms and d be the common difference, then $\begin{aligned}&a_n=1=a+(n-1)d=11\\ &\Rightarrow1+(n-1)d=11\\ &\Rightarrow(n-1)d=11-1\\ &\Rightarrow(n-1)d=10\ldots\\ &S_n=\frac{n}{2}[2a+(n-1)d]=36\\ &\Rightarrow\frac{n}{2}[2\times1+10]=36\quad[\text{ From }(1)]\\ &\Rightarrow n(2+10)=72\\ &\Rightarrow12n=72\\ &\Rightarrow n=\frac{72}{12}\\ &\Rightarrow n=6\end{aligned}$

Related Questions On Progressions


How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22
B. 25
C. 23
D. 24
Show Answer

Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5
B. 6
C. 4
D. 3
Show Answer

Find the 15th term of the sequence 20, 15, 10 . . .

A. -45
B. -55
C. -50
D. 0
Show Answer

The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600
B. 765
C. 640
D. 680
Show Answer



More Related Questions On Progressions