Question

(3) Calculate the difference between the sum of the first 20 terms of the
arithmetic sequences 6, 10, 14, ... and 15, 19, 23,...​

Answer 1

Step-by-step explanation:

=n(2n+4)

2n

2

+4n

(b) For the sum to be 240 from the beginning

240=n

2

+4n

⇒240=n(2n+4)

⇒240=n(2n+4)

⇒120=n(n+2)

⇒n

2

+2n−120=0

⇒n

2

+12n−10n−120=0

⇒n(n+12)−10(n+12)=0

⇒(n+12)(n−10)=0

∴ n=−12,10

10 terms should be added to make the sum to be 240

(c) To make the sum to be 240, 'n' should be natural number.

250=n(2n+4)

⇒125=n(n+2)

⇒n

2

+2n−125=0

⇒n

2

+n−125=0

n=

2

−1

1−4×125

Since n is not a natural number, therefore