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) $S_{n} =\frac{a_{1} + a_{n} }{2} * n$

Solve for last term:   $a_{20}$ = 2(20) + 4 = 44

$S_{20} =\frac{a_{1} + a_{20} }{2} * 20$

    $=\frac{6 + 44}{2} * 20$

    $=\frac{50}{2} * 20$  

   = 25 * 20

   = 500

Answer: $S_{20}$ = 500