Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

475,512 users

Arithmetic Sequence Question Math?

0 votes

Four terms in arithmetic progression have sum of 28. Product of the extreme terms and that of the middle terms are in the ratio 5:6. Find the largest term? 

asked Jul 5, 2014 in ALGEBRA 1 by anonymous

1 Answer

0 votes

Let the numbers be (a- 3d), (a - d), (a + d), (a + 3d).

The difference between thenumbers is 2d.

Sum  of the numbers = 28.

∴ (a- 3d) + (a - d) + (a + d) + (a + 3d) = 28

4a = 28

a = 28/4 = 7.

Product of the extreme terms and that of the middle terms are in the ratio 5:6.

∴ (a- 3d)(a + 3d) / (a - d)(a + d) = 5/6

(a2 - 9d2) / (a2 - d2) = 5/6

6(a2 - 9d2) = 5(a2 - d2)

6a2 - 54d2 = 5a2 - 5d2

a = - 5d2 + 54d2

a = 49d2

(7d)2 = a2

7d = √a2

7d = a

d = a/7 = 7/7 = 1.

Therefore the numbers are (a- 3d) = 7-3 = 4, (a - d) = 7-1= 6, (a + d) = 7+1 = 8, (a + 3d) = 7+3 = 10.

Therefore the largest number is 10.

answered Jul 5, 2014 by joly Scholar

Related questions

asked Jan 3, 2018 in ALGEBRA 2 by anonymous
asked Jan 3, 2018 in ALGEBRA 2 by anonymous
asked Jan 3, 2018 in ALGEBRA 2 by anonymous
...