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:

d =  2

Step-by-step explanation:

a1​=5 (a1​+a2​+a3​+a4​) = 2a5​+a6​+a7​+a8​​  (a1​+(a1​+d)+(a1​+2d)+(a1​+3d)) = 2(a1​+4d)+(a1​+5d)+(a1​+6d)+(a1​+7d)​  4a1​+6d=(4a1​+22d)/2 4⋅ 5+6d=(4⋅ 5+22d)/2  4⋅ 5+6⋅ d=(4⋅ 5+22⋅ d)/2  10d=20  d=1020​=2  d=2

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!



Showing 1 comment:
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





Tips for related online calculators
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Grade of the word problem:

Related math problems and questions: