Question

The sum of the first three terms of the arithmetic progression is 30 and the sum of the squares of the first term and the second term of the same progression is 116. Find the seventh term of the progression if its fifth term is known to be exactly divisible by 14.

• A. 36
• B. 40
• C. 43
• D. 22

Answer 1

The correct option is B 40

Since the sum of the first three terms of the A.P. is 30, the average of the A.P. till 3 terms would be $\frac{30}{3}=10$. The value of the second terms would be equal to this average and hence the second term is 10. Using the information about the sum of squares of the first and second terms being 116., we have that the first term must be 4. Thus, the A.P. has a first term of 4 and a common difference of 6. The seventh term would be 40.