sequence

[sq720]

if the terms of a sequence are t1, t2, t3, tn, what is the value of n?

a.) the sum of the n terms is 3,124
b.) The average of the n terms is 4

C

[DanaJ]

You have a series of terms t1, t2, .... tn. Your goal is to figure out the value of n, meaning that you need to find out how many terms there are in the series.

1. tells you that t1 + t2 + ... + tn = 3124. This really doesn't help much: for all you know, you could have 3124 terms each equal to 1 or three terms t1 = 3000, t2 = 120 and t3 = 4.

2. again, this doesn't help much. The average will be (t1 + t2 + ... + tn)/n, but there's no way of figuring out n without further info. Knowing the average of the series doesn't shed light on the number of terms. You could have two terms t1 = 3 and t2 = 5 or you could have four terms t1 = 2, t2 = 3, t3 = 5 and t4 = 6.

But put the two together and you have something. You know that the average of a set of terms is equal to the sum of the terms divided by the number of terms This is why the number of terms will be (sum)/(average). So your n will be 3124/4 = 781.