MATH 140 Class Exercise #2 Sequences Names__________________

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1. Arithmetic Sequences. We found that in an arithmetic sequence with initial term a and common difference d the nth term is always given by .

a) Find the 100^th term of the arithmetic sequence that begins 5,12,19,… ___________

b) How many terms are there in the sequence 5,12,19, …,726 ? __________

c) We developed the following method to sum arithmetic sequences. Suppose we wish to add the following sequence: . We actually write out the sum twice in opposite orders and add vertically:

Thus twice the sum, 2S, is 68 times the number of terms in the sequence. There are 11 terms. 2S = 11x68 = 748. Thus the original sum is 374.

Find ____________

d) In this part we are concerned with the sequence 1,3,5,7,.., the arithmetic sequence of consecutive odd numbers starting at 1.

What is a? ________

What is d? ________

What is the nth term (in terms of n) of the sequence 1, 3, 5, …? ___________

Find the following sums:

What pattern do you see in the sums?

Let be the nth term in the sequence 1, 3, 5, 7, …. Now apply our technique to find the sum of . Your answer should be in terms of n.