The sum of the first ten terms of an arithmetic Progression is 400. If the sum of the first 6
terms of the same series is 120, find the 15th term.

345.

Explanation:

Sum of n terms = n/2[2a1 + (n-1)d]

So 400 = 10/2(2a1 + 9d) and

120 = 3(2a1 + 5d)  so we have the system:

400 = 10a1 + 45d A

120  = 6a1 + 15d    B         multiply this by 3:

360  = 18a1 + 45D     Subtract this from equation A:

40 = -8a1

a1 = -5

So plugging this value into B:

d =  (120 - 6*-5) / / 6

= 150/6 = 25.

15th term = a1 + (n - 1)d

= -5 + (15-1)25

=  345.

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