Question

The sum of the first three terms of the arithmetic progression is 24 and the sum of the squares of the first term and the second term of the same progression is 80.Find the 8^th term of the progression if its fifth term is known to be exactly divisible by 10. 

(a) 32 

(b) 36 

(c) 40 

(d) 42

Answer 1

Correct option (a) 32

Explanation:

Since the sum of the first three terms of the AP is 24, the average of the AP till 3 terms would he 24/3 = 8. Value of the second term would be equal to this average and hence the second term is 8. Using the information about the sum of squares of the first and second terms being 80, we have that the first term must be 4. Thus, the AP has a first term of 4 and a common difference of 4. The seventh term would be 32.