Question

The number of terms of an A.P. 3, 7, 11, 15... to be taken so that the sum is 406 is​

Answer 1

Answer:

n = 14

Step-by-step explanation:

ANSWER: n = 14

Sn = 406

a = 3

d = 7-3 = 4

n = ?

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

406 = n/2 ( 2 x 3 + (n-1) 4)

406 x 2 = n ( 6+ 4n -4)

812 = n (2 + 4n)

812 = 2n + 4n^2

4n^2. + 2n - 812 = 0.

2n^2 +n - 406 = 0. ....[Taking 2 as common]

2n^2 - 28n +29n - 406 = 0.

2n (n - 14) + 29 (n - 14) = 0

(2n + 29) (n-14) = 0.

2n + 29 = 0

n = -29/2

n - 14 = 0

n = 14

SINCE VALUE OF n CANNOT BE IN FRACTION, THEREFORE n = 14.

HOPE IT HELPS

Answer 2

Answer:

Since the value of N cannot be fraction, therefore n=14

Hope this helps you