Arithmetic Sequences:

Question

1. The first term of an arithmetic sequence is -8 and the common difference is 3.

(a) Find the seventh term of the sequence.

(b) The last term is 100. How many terms are there?

Answer 1

a=-8

d=3

n=7

an=a+(n-1)d

    =-8+6.3

    =10

Seventh term=10

 100=-8+(n-1)3

       =-8+3n-3

3n=111

 n =37

So,37 terms

Answer 2

You may list the sequence as :

 

Term:   1    2    3    4    5    6     7    8    9    10   11   12   13    14    15   16   17   18   19  20
Value: -8   -5   -2    1   4     7   10  13   16   19   22   25   28    31    34   37   40   43   46  49
 
Term:  21   22   23   24   25   26   27   28   29   30   31   32   33   34   35   36    37
Value:  52   55   58   61  64   67   70   73   76   79   82   85   88   91   94   97   100

 

But you should soon save time by learning the formula:

             Term(n) = Term (1) + (n-1)*Distance              Check it out on some samples!

 

And, given an "n," you can find the value of that term, or, as in this problem, given the value, you can find the term.