Question

How many terms of the series 15+12+9... must be taken to make 15?Explain with double answers.

Answer 1

Answer:

10

Step-by-step explanation:

Given  

How many terms of the series 15+12+9... must be taken to make 15?

Given  

15 + 12 + 9 + …..

To find using A.P

To find n, a = 15, d = 12 – 15 = - 3

Sn = n/2 [ 2a + (n – 1)d]

Now Sn = 15

n/2 [2(15) + (n – 1)(-3)] = 15

n(30 – 3n + 3) = 30

n(33 – 3n) = 30

33n – 3n^2 = 30

3n^2 – 33n + 30 = 0

n^2 – 11n + 10 = 0

(n – 1)(n – 10) = 0

n = 1, 10

So n = 10