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.
Your answer:
Your answer:
.webp)
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
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 a solution? Or do you have a quadratic equation?
You need to know the following knowledge to solve this word math problem:
algebraarithmeticGrade of the word problem
Related math problems and questions:
- The common difference
Find the common difference of an arithmetic progression (AP), whose 1st term is 5 and the sum of its 1st 4 terms is half the sum of the next four terms. - The sum 39 The sum of the first six terms of the arithmetic sequence is 72, and the second term is seven times the fifth term. Find the first term and the AP difference.
- Common difference
The 4th term of an arithmetic progression is 6. Find the common difference if the sum of the 8th and 9th terms is -72. - Two terms and d
The 8th term of an arithmetic progression is 17 and its 14th term is 29. Find the common difference. - The sum 23
The sum of the first 10 terms of an arithmetic sequence is 530. What is the first term if the last term is 80? What is the common difference? - AP - general term Find the sum of the first 12 terms of the arithmetic sequence whose general term is an=3n+5.
- The product 9 The product of the third and second terms of the arithmetic progression is 3000. If the common difference is 10, find the first term.
