sequence and series

[rahul.s]

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]

[ajith]

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)

[rahul.s]

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?

[ajith]

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

Yes, it is a standard formula for evenly spaced numbers in a series (in More technical terms an Arithmetic progression)