Question

2 + 4 + 6 ...... + 2n = 240 What is the value of n?​

Answer 1

Answer:

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

where a=2

d=2

n² + n - 240

n = 30 ; n = -32

negative value rejected

Answer 2

Answer:

The value of n=15

Solution:  

Given Data: 2 + 4 + 6 ...... + 2n = 240

According to the question:

To Find: Find the value of n

Step 1:

Given:-  

Sum of first n terms of an AP 2, 4, 6, is = 240

Here,

a = first term = 2

d = common difference

Step 2:

= a2 - a1 = 4 - 2 = 2

Sn $=\frac{n}{2}$  [2a + (n - 1)d]

Step 3:

240$=\frac{n}{2}$ [(2 $\times$ 2) + (n - 1)2]

240$\times$ 2 = n (4 + 2n - 2)

Step 4:

480 = n(2 + 2n)

480 = 2n + $2n^2$

$2n^2$ + 2n - 480 = 0

Step 5:

Taking 2 as common we get,

2($n^2$ + n - 240) = 0

$n^2$ + n - 240 = 0

Step 6:

Splitting the middle term,

$n^2$  + (16n - 15n) - 240 = 0

$n^2$ + 16n - 15n - 240 = 0

Step 7:

n (n + 16) - 15(n + 16) = 0

(n + 16) (n - 15) = 0

Step 8:

Result:

n = -16 or n = 15

Since n can't be negative so n = 15.