# Mathematics

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

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1. a+5d = 37
6/2 (2a+5d) = 147
Now just solve for a and d, and
S15 = 15/2 (2a+14d)

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2. 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

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3. a+5d = 37
12+5d = 37
5d = 37- 12 = 25
5d = 25
d = 5

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4. 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.

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