Question

if the first four termsof an ap are a,2a,b and a-6-b for some numbers a and b then the sum of first 100 terms of sequence is

Answer 1

we have
2a - a = b - 2a (difference is same in AP)
a = b - 2a
3a = b ..... (1)

Therefore, four terms are
a, 2a, 3a, -6 - 2a

Now,
-6 - 2a - 3a = 3a - 2a (common difference)
-6 - 5a = a
-6 = 6a
a = -1 .....(2)

Now four terms are
-1, -2, -3, -4

Therefore, a=-1, d=-1, n=100
Sum of 100 terms = 100/2{ 2(-1) + (100-1)(-1) }
= 50(-2 -99)
= 50 X -101
= -5050