Question

If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?

Answer 1

Answer:

Step-by-step explanation:

Sum of 11 terms of an AP equals the sum of 19 terms of the same AP.

S11 = (11/2)[2a+10d] …(1)

S19 = (19/2)[2a+18d] …(2)

Equate (1) and (2)

(11/2)[2a+10d] = (19/2)[2a+18d], or

22a+110d = 38a+342d, or

16a = -232d, or a = -(232/16)d

S30 = (30/2)[2a+29d]

= 15[-(464d/16) + 29d]

= (15/3)[-29d+29d]

= 0

The sum of the 30 terms of the AP is 0.

⚡Hope it helps u.⚡

Answer 2

Answer:

Sum of 1st 30 terms is 30