1. Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____
Given the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula.
a 1 = 28, d = ) a 1 = −38, d = −100
1st Term:_____
2nd Term:_____
3rd Term:_____
4th Term:_____
5th Term:_____
1st Term:_____
2nd Term:_____
3rd Term:_____
4th Term:_____
5th Term:_____

2. Let’s Take it up a notch
Given a term in an arithmetic sequence and the common difference find the first term and the explicit formula.
1) a 38 = −53.2, d = − ) a 40 = −1191, d = −30

3. Warm Up(Answers) An = d(n-1) + a1 1st Term: 28 An = 10(n-1) + 28
Given the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula.
a 1 = 28, d = ) a 1 = −38, d = −100
An = d(n-1) + a1
An = 10(n-1) + 28 Or
= 10n –
= 10n + 18
An =10n + 18
An = d(n-1) + a1
An = -100(n-1) - 38 Or
= -100n
= -100n + 62
An =-100n + 62
1st Term: 28
2nd Term: = 38
3rd Term: = 48
4th Term: = 58
5th Term: = 68
1st Term: -38
2nd Term: = -138
3rd Term: = -238
4th Term: = -338
5th Term: = -438

4. Let’s Take it up a notch (Answers)
Given a term in an arithmetic sequence and the common difference find the first term(a 1) and the explicit formula. 1) a 38 = −53.2, d = −1.1 2) a 40 = −1191, d = −30
An = d(n-1) + a1
A38 = -1.1(n-1) + a1
A38 = -1.1(38-1) + a1
-53.2= -1.1(37) + a1
-53.2 = a1
12.5 = a1
a1 = d= -1.1
An = d(n-1) + a1
An = -1.1(n-1) Or
= -1.1n
= -1.1n
An = -1.1n
An = d(n-1) + a1
A40 = -30(n-1) + a1
A40 = -30(40-1) + a1
-1191= -30(39) + a1
-1191 = a1
-21 = a1
a1 = d= -30
An = d(n-1) + a1
An = -30(n-1) – 21 or
An = -30(n-1) - 21
= -30n
= -30n + 9
An = -30n + 9