### The first term of an Arithmetic Progression is 22 and the last term is -11. If the sum is 66, the number of terms in the sequence are:

A. 10 B. 12 C. 9 D. 8 Answer: Option B

### Solution(By Apex Team)

Number of terms = n (let) First term (a) = 22 Last term (l) = – 11 Sum = 66 Sum of an AP is given by: \begin{aligned}&=\text{ Number of terms }\times\frac{\text{ First term }+\text{ Last term }}{2}\\ &66=\mathrm{n}\times\frac{\mathrm{a}+\mathrm{l}}{2}\\ &66=\mathrm{n}\times\frac{22-11}{2}\\ &66=\mathrm{n}\times\frac{11}{2}\\ &\mathrm{n}=\frac{66\times2}{11}\\ &\mathrm{n}=12\\ &\text{No. of terms}=12\end{aligned}

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

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

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