Question

How many terms of the A.P. 20, 19/3, 18/2, ... be taken so that their sum is 300?​

Answer 1

Answer:

25 and 36, sum of all terms from 26th to 36th is zero.

Answer 2

Answer:

36 or 25

Step-by-step explanation:

a = 20, d = -2/3

Sn = n/2 [2a + (n-1)d]

300 = n/2 [2×20 + (n-1) ( -2/3)

300 = n/2 [ 40 -2/3n + 2/3]

300 = n/2 [ 122-2n/3]

300 = n(122 - 2n)/ 2×3

300 = 122n - 2n^2/6

300×6 = 122n - 2n^2

1800 = 122n - 2n^2

2n^2 - 122n + 1800 = 0

splitting middle term

2n^2 - 50n -72n +1800 =0

2n( n - 25) - 72 ( n-25) =0

(2n - 72) ( n - 25) =0

2n-72=0 or n-25=0

n= 72/2 or n = 25

n= 36 or n = 25

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