Find the exact value (either decimal or fractional form) of the first term of an arithmetic sequence if the sum of the first 100 terms is 7099.5 and the sum of the next 100 terms is 20799.

Answer 1

We find a from a system:
a +a+99d =7099.5
a+100d+a+199d=20799

We subtract from the 2nd the 1st:

200d=13699.5
d=68.4975

2a+99x68.4975=7099.5
a=159.12375 (0.12375=99/800)

Answer 2

Ummm.

Sn = n(a1 + an)/2
S100 = 100(a1 + a100)/2
= 50(a+a+99d)
= 100a + 4950