GATE Civil 2020 Set 1 | GA Question: 8

Question

Insert seven numbers between $2$  and $34$, such that the resulting sequence including $2$ and $34$  is an arithmetic progression. The sum of these inserted seven numbers is  ______.

• A. $120$
• B. $124$
• C. $126$
• D. $130$

Answer 1

We can insert the seven numbers in such a way that, so we get the arithmetic progression including $2$ and $34.$

 We get the arithmetic progression $2,6,10,14,18,22,26,30,34$

The inserted seven numbers are $6,10,14,18,22,26,30$

Here, $a = 6,d = 10-6 = 4,l = 30,n = 7$

$\therefore$ The sum of the arithmetic progression $S_{7} = \frac{7}{2}\left(6 + 30 \right) = 7 \cdot 18 = 126.$

So, the correct answer is $(C).$