Question

Find the first four and stated term given the arithmetic sequence, with a1 as the 1st term.

Answer 1

To find the first four terms and stated term you substitute the n in each equation sequence for: 1, 2 , 3, 4 and stated term:

5)

`a_n=13.3+5.9n`

First term: n=1

`a_1=13.3+5.9(1)=19.2`

Second term: n=2

`a_2=13.3+5.9(2)=25.1`

Third term: n=3

`a_3=13.3+5.9(3)=31`

Fourth term: n=4

`a_4=13.3+5.9(4)=36.9`

11th term: n=11

`a_(11)=13.3+5.9(11)=78.2`Then, the first four terms are: 19.2, 25.1, 31, 36.9 and the 11th term is 78.2

6)

`a_n=12.4+5.5n`

First term: n=1

`a_1=12.4+5.5(1)=17.9`

Second term: n=2

`a_2=12.4+5.5(2)=23.4`

Third term: n=3

`a_3=12.4+5.5(3)=28.9`

Fourth term: n=4

`a_4=12.4+5.5(4)=34.4`

16th term: n=16

`a_(16)=12.4+5.5(16)=100.4`Then, the first four terms are: 17.9, 223.4, 28.9, 34.4 and the 16th term is 100.4

7)

`a_n=3+6n`

First term: n=1

`a_1=3+6(1)=9`

Second term: n=2

`a_2=3+6(2)=15`

Third term: n=3

`a_3=3+6(3)=21`

Fourth term: n=4

`a_4=3+6(4)=27`

14th term: n=14

`a_(14)=3+6(14)=87`Then, the first four terms are: 9, 15, 21, 27, and the 14th term is 87

8)

`a_n=24.5+5.0n`

First term: n=1

`a_1=24.5+5.0(1)=29.5`

Second term: n=2

`a_2=24.5+5.0(2)=34.5`

Third term: n=3

`a_3=24.5+5.0(3)=39.5`

Fourth term: n=4

`a_4=24.5+5.0(4)=44.5`

19th term: n=19

`a_(19)=24.5+5.0(19)=119.5`Then, the first four terms are: 29.5, 34.5, 39.5, 44.5, and the 19th term is 119.5