Question

problems 5 - 8, write the first five terms of each

1. $a_n = 7 + 5n$
2. $a_n = 120 - 8n$

problems 9 - 12, find the $28^{\text{th}}$ term of each se

1. 22,25,28,31, ...
2. 1.7,1.9,2.1,2.3, ...

Explanation:

Problem 5: $a_n = 7 + 5n$

Step1: Substitute $n=1$

$a_1 = 7 + 5(1) = 12$

Step2: Substitute $n=2$

$a_2 = 7 + 5(2) = 17$

Step3: Substitute $n=3$

$a_3 = 7 + 5(3) = 22$

Step4: Substitute $n=4$

$a_4 = 7 + 5(4) = 27$

Step5: Substitute $n=5$

$a_5 = 7 + 5(5) = 32$

Problem 7: $a_n = 120 - 8n$

Step1: Substitute $n=1$

$a_1 = 120 - 8(1) = 112$

Step2: Substitute $n=2$

$a_2 = 120 - 8(2) = 104$

Step3: Substitute $n=3$

$a_3 = 120 - 8(3) = 96$

Step4: Substitute $n=4$

$a_4 = 120 - 8(4) = 88$

Step5: Substitute $n=5$

$a_5 = 120 - 8(5) = 80$

Problem 9: $22,25,28,31,...$

Step1: Define arithmetic sequence formula

Arithmetic sequence: $a_n = a_1 + (n-1)d$, where $a_1=22$, $d=3$

Step2: Simplify the sequence formula

$a_n = 22 + (n-1)(3) = 3n + 19$

Step3: Substitute $n=28$

$a_{28} = 3(28) + 19 = 84 + 19 = 103$

Problem 11: $1.7,1.9,2.1,2.3,...$

Step1: Define arithmetic sequence formula

Arithmetic sequence: $a_n = a_1 + (n-1)d$, where $a_1=1.7$, $d=0.2$

Step2: Simplify the sequence formula

$a_n = 1.7 + (n-1)(0.2) = 0.2n + 1.5$

Step3: Substitute $n=28$

$a_{28} = 0.2(28) + 1.5 = 5.6 + 1.5 = 7.1$

Answer:

Problem 5: 12, 17, 22, 27, 32
Problem 7: 112, 104, 96, 88, 80
Problem 9: 103
Problem 11: 7.1