Question

Determine the indicated term in the following arithmetic sequences.

1.) a subscript 5: {2, 5, 8, ...}
2.) a subscript 20: {4, 8, 12, ...}
3.) a subscript 18: {0,20,40,60, ...}

Answer 1

`a_5= 14`

`a_(20)= 80`

`a_(18)= 340`

Explanation:

Solving (a):

We have:

`a_1=2` --- first term

`d = 5 -2 = 3` common difference

The 5h term is:

`a_n= a_1 + (n - 1)d`

`a_5= 2+ (5 - 1)*3`

`a_5= 14`

Solving (b):

We have:

`a_1 = 4` --- first term

`d = 8 -4 = 4` common difference

The 20h term is:

`a_n= a_1 + (n - 1)d`

`a_(20)= 4+ (20 - 1)*4`

`a_(20)= 80`

Solving (c):

We have:

`a_1 = 0` --- first term

`d = 20 -0 = 20` common difference

The 18th term is:

`a_n= a_1 + (n - 1)d`

`a_(18)= 0+ (18 - 1)*20`

`a_(18)= 340`