sum of series

Expert replies

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 1:11 pm

Assume the given sum of the series, 7.5 + 15.5 + 10.5 + 13.0 + 13.5 + 10.5....+ x – y + z is
20634, (x, y, z > 0) then what is the value of the expression (2x + 3y + 5z)?

1084
1284
1464
1684
None of these

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 1:11 pm

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Tue Feb 09, 2010 2:02 pm

shashank.ism wrote:Assume the given sum of the series, 7.5 + 15.5 + 10.5 + 13.0 + 13.5 + 10.5....+ x – y + z is
20634, (x, y, z > 0) then what is the value of the expression (2x + 3y + 5z)?

1084
1284
1464
1684
None of these

alternatively we find that we have 2 series.Identifying them,we can solve the question.
1st series = 7.5 + 10.5 + 13.5 + ..... +x +z = 7.5 + (7.5 + 3)+..... Hence, a =7.5,n=3
2nd series = 15.5 + 13.0 + 10.5 +.... .Hence,b=15.5 , n= -2.5
So,we can get x,y and z using the formula of sum of series till x terms = ax + n*(x-1)(x)/2

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