Question

How many terms of the series 148 + 146 + 144 + 142 + ... must be taken to
have their sum amount to 3000 ? Explain the double answer.
[Ans. 24 or 12511. ​

Answer 1

Answer:

The given series is an arithmetic profession

a= 148 (first term)

d = -2 (common difference)

sum of n terms in AP = n/2 [2a + (n-1)d]

3000 = n/2 [ (2)(148) + (n-1)(-2)

6000 = n (296 - 2n +2)

6000 = - 2n^2 + 298n

2n^2 - 298n + 6000 = 0

n^2 - 148n + 3000 = 0

n^2 - 24n - 125n +3000 = 0

n ( n -24) - 125 ( n - 24) = 0

( n- 24) ( n- 125) = 0

this means n = 24 or 125

Hope this helps. Good luck!