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Sequence - 4 (Posted on 2006-03-23) Difficulty: 3 of 5
The number of terms of an Arithmetic Progression is even.

The sum of the terms in the odd places (First term + Third Term + Fifth Term + ...and so on) is 24;

The sum of the terms in the even places (Second Term + Fourth Term + Sixth Term + ... and so on) is 30; and

The last term exceeds the first by 21/2, then:

What is the arithmetic progression?

No Solution Yet Submitted by Ravi Raja    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 4

The sequence is 1.5, 3, 4.5, 6, 7.5, 9, 10.5, 12.

I happened to just guess it, it seemed natural, but if you wanted to find it by mathematical means you can use the following formulas (all from the clues given):

f = first term in sequence
n = number of terms in sequence
d = difference between terms

d(n-1) = 10.5
(dn)/2 = 6
(2f+10.5)(n)/2 = 54

When you solve those equations you get f = 1.5, d = 1.5, n = 8.

 


  Posted by tomarken on 2006-03-23 09:11:16
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