3. What is the sum of the first n odd numbers?
4. Find the 14th term of the sequence 8/9, -4/3, 2,……………………
5. Find the sum of the 1st ten terms of a G. P 8+4+2+…………………..
6. Calculate the sum to infinity of the series 2+1/2+1/4+1/12+………………..

3. Odd numbers take the form for . So the sum of the first (positive) odd integers is

Recall that

4. The sequence is geometric with common ratio :

and so on. Then the th term in the sequence is given by the rule

and so the 14th term in the sequence is

5. The sequence is geometric with ratio , so that the th term in the sequence is

The sum of the first 10 terms is

We then have

6. The th term of the sequence {1/2, 1/4, 1/12, ...} is given by

so the given sum can be written as

Recall that

so the given sum is equal to

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)