Question

For the sequence given by a_n=2n+4 , answer the following:

a. Write the first five terms of the sequence

b. Find the sum of the first 20 terms

Answer 1

a. 6, 8, 10, 12, 14

Work:

a_1 = 2(1) + 4

a_1 = 6

a_2 = 2(2) + 4

a_2 = 8

a_3 = 2(3) + 4

a_3 = 10

a_4 = 2(4) + 4

a_4 = 12

a_5 = 2(5) + 4

a_5 = 14

b. 500

Work:

Since the common difference is 2, we can add 2 to each number until we reach the 20th term.

6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 = 500

Answer 2

a)
`a_(n)` = 2(n) + 4

`a_(1)` = 2(1) + 4 = 6

`a_(2)` = 2(2) + 4 = 8

`a_(3)` = 2(3) + 4 = 10

`a_(4)` = 2(4) + 4 = 12

`a_(5)` = 2(5) + 4 = 14

Answer: 6, 8, 10, 12, 14

b)
`S_(n) =(a_(1) + a_(n) )/(2) * n`

Solve for last term:
`a_(20)` = 2(20) + 4 = 44

`S_(20) =(a_(1) + a_(20) )/(2) * 20`

`=(6 + 44)/(2) * 20`

`=(50)/(2) * 20`

= 25 * 20

= 500

Answer:
`S_(20)` = 500