Question

Choose the correct answer in each of the following questions:

The 5th term of an AP is −3 and its common difference is −4. The sum of its first 10 terms is [CBSE 2011]

(a) 50 (b) −50 (c) 30 (d) −30

Answer 1

Let a be the first term of the AP.

Here, d = −4

$$\begin{gathered} a_5=-3\left(\mathrm{Given}\right) \\ \Rightarrow a+\left(5-1\right)\times \left(-4\right)=-3\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow a-16=-3 \\ \Rightarrow a=16-3=13 \end{gathered}$$

Using the formula, $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$, we get

$$\begin{gathered} S_{10}=\frac{10}{2}\left[2\times 13+\left(10-1\right)\times \left(-4\right)\right] \\ =5\times \left(26-36\right) \\ =5\times \left(-10\right) \\ =-50 \end{gathered}$$

Thus, the sum of its first 10 terms is −50.

Hence, the correct answer is option B.