Question

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.​

Answer 1

Answer:

345.

Step-by-step 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.