sequence and series

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 am; Thanked: 17 times; Followed by:1 members

sequence and series

by rahul.s » Tue Jan 26, 2010 3:33 am

Sequence X consists of 825 terms, and each term after the first term is 5 more than the preceding term. What is the 500th term of sequence X?

(1) The 515th term of sequence X is -98

(2) The first term of sequence X is -2668

[spoiler]OA is D, but i'd like to know how you'd derive the numbers?[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Tue Jan 26, 2010 3:33 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Tue Jan 26, 2010 4:09 am

rahul.s wrote:Sequence X consists of 825 terms, and each term after the first term is 5 more than the preceding term. What is the 500th term of sequence X?

(1) The 515th term of sequence X is -98

(2) The first term of sequence X is -2668

[spoiler]OA is D, but i'd like to know how you'd derive the numbers?[/spoiler]

The question refers to an arithmetic progression

say a is the first term, second term is a+d third term is a +2d and so on ....

the n th term of an arithmetic progression with a as the first term and d as the common difference is = a + (n-1)*d ---1(1)

Now the question says d = 5 and total number of terms = 825

the 500 term of such an arithmetic progression is a + (n-1)*d = a + 499*5 -----(2)

Now we need to find a from the supporting statements

1) a + 514*5 = -98

We can find out a and 500th term using (2)

2) a = -2668

We can find out 500th term using (2)

Always borrow money from a pessimist, he doesn't expect to be paid back.

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 am; Thanked: 17 times; Followed by:1 members

by rahul.s » Wed Jan 27, 2010 3:07 am

ajith wrote:
rahul.s wrote:Sequence X consists of 825 terms, and each term after the first term is 5 more than the preceding term. What is the 500th term of sequence X?

(1) The 515th term of sequence X is -98

(2) The first term of sequence X is -2668

[spoiler]OA is D, but i'd like to know how you'd derive the numbers?[/spoiler]
The question refers to an arithmetic progression

say a is the first term, second term is a+d third term is a +2d and so on ....

the n th term of an arithmetic progression with a as the first term and d as the common difference is = a + (n-1)*d ---1(1)

is this a general rule for evenly spaced numbers in a series?

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members