Question

The sum of the first and the eighth terms of an A.P. is $24$ then the sum of the fourth and fifth terms of the A.P. will be

• A. $12$
• B. $24$
• C. $18$
• D. None of these

Answer 1

The correct option is B

$24$

Arithmetic progression (A.P):

Arithmetic progression is defined as a series in which the difference between any two consecutive terms is constant throughout the series. The constant difference is called the common difference.

The explanation for the correct option: (Option B)

Formula:

We know that the $n^{th}$term of an A.P. with the first term $a$and the common difference $d$is given by

$a_n=a+(n-1)d$

Calculation:

Let the first term of the A.P. be $a$and common difference $d.$

Hence,

$$\begin{gathered} a_8=a+(8-1)d \\ =a+7d \end{gathered}$$

According to the question:

$$\begin{gathered} a+a_8=24 \\ \Rightarrow a+a+7d=24 \\ \Rightarrow 2a+7d=24.......\left(i\right) \end{gathered}$$

We know,

$$\begin{gathered} a_4=a+(4-1)d=a+3d \\ {a}_5=a+(5-1)d=a+4d \end{gathered}$$

Now, $$\begin{gathered} a_4+a_5=a+3d+a+4d \\ =2a+7d \\ =24(Byeqi) \end{gathered}$$

Conclusion:

Hence, 24 (Option B ) is our correct option.