Question

FIND THE COMMON DIFFERENCE OF AN AP WHOSE FIRST TERM IS 100 AND THE SUM OF THE FIRST 6 TERMS IS 5 TIMES THE SUM OF THE NEXT 6 TERMS.

Answer 1

SUM(1 to 6) = a + a + d + a + 2d + a + 3d + a + 4d + a + 5d 
= 6a + 15d 
= 600 + 15d       .........(1)

Sum(7 to 12)

T7 = 100 + 6d 
T12 = 100 + 11d 
sum from T7 to T12 = 600 + (6 + 7 + 8 + 9 + 10 + 11)d 
= 600 + 51d  ...........(2)
equating 1 and 2, we get;
600 + 15d = 5(600 + 51d) 
120 + 3d = 600 + 51d 
48d = – 480 
d = – 10 

Answer 2

Answer:

Here is your answer

d=-10