If the sixth term of an A.P is 37 and the sum of the first sixth term is 147.find the first term and the sum of the first 15 terms
a+(n-1)d =37
n/2 (2a+(n-1)d=147
So a+5d=37 eqn 1=37
3(2a +5d) eqn 2=147
Use elimination
a= 12
a+5d = 37
6/2 (2a+5d) = 147
Now just solve for a and d, and
S15 = 15/2 (2a+14d)
a+5d = 37
12+5d = 37
5d = 37- 12 = 25
5d = 25
d = 5
n/2 (2a+ (n-1)d
15/2 [2(12) +14d]
15/2 [24 + 14×5]
15/2 [24 + 70]
15/2 [ 94]
15× 47= 705.