# The common difference 2

Find the common difference of an arithmetic progression (AP), whose first term is 5 and sum of its first 4 terms is half the sum of the next four terms.

## Correct answer:

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**Dr Math**

Another solution:

first term is 5

sum of its first 4 terms is half the sum of the next four terms.

Let the common difference between d

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

S4=4/2(2*5+(4-1)d)

=2(10+3d)=20+6d

S8-S4=8/2(2*5+7d)-20-6d

=(40+28d-20-6d)

=(20+22d)

As per question,

(20+6d)*2=20+22d

=>40+12d=20+22d

=>10d=20

=>d=2

S4=20+6d =20+6(2)=32

S8-S4=20+22d=20+44=64

first term is 5

sum of its first 4 terms is half the sum of the next four terms.

Let the common difference between d

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

S4=4/2(2*5+(4-1)d)

=2(10+3d)=20+6d

S8-S4=8/2(2*5+7d)-20-6d

=(40+28d-20-6d)

=(20+22d)

As per question,

(20+6d)*2=20+22d

=>40+12d=20+22d

=>10d=20

=>d=2

S4=20+6d =20+6(2)=32

S8-S4=20+22d=20+44=64

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