# arithmetic

posted by .

find the common difference of A.P whose first term is 5 and the sum of its first 4 terms is half the sum of next 4 terms

• arithmetic -

Let the common difference be d.
The sum of the first four terms is
5 + (5+d) + (5+d+d) + (5+d+d+d)
= 20 + 6d
The sum of the next 4 terms is
5+4d + 5+5d + 5+6d + 5+7d = 20 + 22d

You have been told that
20 +6d = (1/2)(20 + 22d)= 10 + 11d
Therefore
5d = 10
d = 2

Check: does
5+7+9+11 = (1/2)(13+15+17+19) ?
32 = (1/2)(64)

• arithmetic -

## Similar Questions

1. ### Precalculus

The 8th term in an arithmetic sequence is 5, and the sum of the first 10 terms is 20. Find the common difference and the first term of the sequence. Alright so in an arithmetic squence the difference d between any two successive numbers …
2. ### math

1) If the sum of the first n terms of a series is Sn where Sn=2n²-n, (a)prove that the series is an AP, stating the first term and the common difference; (b)find the sum of the terms from the 3rd to the 12th inclusive 2) In an AP …
3. ### Math

1) If the sum of the first n terms of a series is Sn where Sn=2n²-n, (a)prove that the series is an AP, stating the first term and the common difference; (b)find the sum of the terms from the 3rd to the 12th inclusive 2) In an AP …
4. ### maths

1) The first term of arithmetic progression is -20 and the sum of it's term is 250. find it's last term if the number of it's terms is 10 2) Find the fifth term from the arithmetic progression -12, -9, -6 hence find the sum of it's …
5. ### arithmetic

the sum of the n termsof an ap whose first term is 5 and common difference is 36 is equal to the sum of 2n terms of another AP whose first term is 36 ans common difference is 5. Find n?
6. ### Math(arithmetic & Geometric Series)

1)The sum of 6 terms of an arithmetic series is 45, the sum of 12 terms is -8. Find the first term and the common difference?
7. ### arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term …
8. ### arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term …
9. ### math

The sum of the first 20 terms of an arithmetic series is identical to the sum of the first 22 terms. If the common difference is -2, find the first term.
10. ### Math

An arithmetic progression has 10 terms. Sum of the 10 terms is 220. Sum of the odd terms is 100. Find the first term and common difference.

More Similar Questions