I can see this is an arithmetic sequences worksheet. Let me work through each problem carefully.
Problem 1: Determine if the sequence is arithmetic. If it is, find the common difference.
a) 3, 8, 13, 18, 23, ...
b) -5, -9, -13, -17, -21, ...
c) 4, 6, 9, 13, 18, ...
d) 10, 7, 4, 1, -2, ...
Let me check each:
a) Differences: 8-3=5, 13-8=5, 18-13=5, 23-18=5 ✓ Arithmetic with d=5
b) Differences: -9-(-5)=-4, -13-(-9)=-4, -17-(-13)=-4, -21-(-17)=-4 ✓ Arithmetic with d=-4
c) Differences: 6-4=2, 9-6=3, 13-9=4, 18-13=5 ✗ Not arithmetic (differences are not constant)
d) Differences: 7-10=-3, 4-7=-3, 1-4=-3, -2-1=-3 ✓ Arithmetic with d=-3
Problem 2: Given the explicit formula for an arithmetic sequence that fits the first five terms and the term named in the blank.
a) aₙ = 3 + 5(n-1); Find a₁₀
a₁₀ = 3 + 5(10-1) = 3 + 5(9) = 3 + 45 = 48
b) aₙ = -2 + 2n; Find a₅
a₅ = -2 + 2(5) = -2 + 10 = 8
c) aₙ = 11/2 - n/2; Find a₂₀
a₂₀ = 11/2 - 20/2 = 11/2 - 10 = 11/2 - 20/2 = -9/2
Problem 3: Given the first term and the common difference of an arithmetic sequence that fits the first five terms and the term named in the blank.
a) a₁ = 2, d = 3; Find a₁₀₀
Using formula: aₙ = a₁ + (n-1)d
a₁₀₀ = 2 + (100-1)(3) = 2 + 99(3) = 2 + 297 = 299
b) a₁ = -24, d = 10; Find a₀
a₅₀ = -24 + (50-1)(10) = -24 + 49(10) = -24 + 490 = 466
c) a₁ = 21, d = -4; Find a₀
a₃₀ = 21 + (30-1)(-4) = 21 + 29(-4) = 21 - 116 = -95
Final Answer:
1a) Yes, arithmetic, d = 5
1b) Yes, arithmetic, d = -4
1c) No, not arithmetic
1d) Yes, arithmetic, d = -3
2a) a₁₀ = 48
2b) a = 8
2c) a₂₀ = -9/2
3a) a₁₀₀ = 299
3b) a₀ = 466
3c) a₃₀ = -95
Parent Tip: Review the logic above to help your child master the concept of arithmetic sequence worksheet with answers.
