Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 50, 100, 150, 200, .

Answer 1

50n

Explanation:

This problem can be solved using concept of Arithmetic progression(AP)

In AP series

the series increases or decreases by certain number which is called common difference.

common difference d is given by

d= nth term - (n-1)th term

nth term = a + (n-1)d

where a is the first term of the series

thus series can be a , a+d, a+2d, a+3d, a+4d, ...........a + (n-1)d

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Given series

50, 100, 150, 200

a = 50

to find d lets use 3rd term as nth term and 2nd term as (n-1)th term

d = 150 -100 = 50

Thus,

nth term = 50 + 50(n-1) = 50 + 50n -50 = 50n

50n can represent the position of the term of the sequence.

To validate this lets put n = 4

50*4 = 200 which is the same as the fourth term given in the series.

hence our solution is correct.