Question

What is the common difference of an AP which has its first term as 100 and the sum of its first 6 terms = 5 times the sum of its next six terms?

• A. 12
• B. 15
• C. -10
• D. -2

Answer 1

The correct option is C -10

Option a and b can be eliminated directly, as from the statement sum of its first 6 terms = 5 times the sum of its next six terms, we can deduce that the Common Difference is negative (decreasing AP).

Go from answer options :

Take option c

Sum to $1^{st}$ 6 terms is given by the formula $\frac{n}{2(2a+[n-1\left]d\right)}$

= 3(200-50)= 450

Sum to $2^{nd}$ 6 terms = Sum to 12 terms – sum to 6 terms

= 6( 200-110) -450

= 540 – 450 = 90

5 $\times$ Sum to $2^{nd}$ 6 terms = 450

Hence option c