Solve for the questions below

Question

For each of the following arithmetic sequences,

(a) Write the first six terms of the arithmetic sequence satisfying the given

conditions.

(b) Write a non-recursive formula for the nth term, A_n, of the sequence.

(c) Find the 20th and 50th terms of the sequence.

1. A₁= 8, d= 5
2. A₁=-4, A₂=-1
3. A₃=11, A₄=15
4. A₁=3, A₁₁=58 (Hint: Substitute the two given terms into a non-recursive formula to find d)

Answer 1

For all, need to use a_n = a₁ + d(n-1), where d is the difference between terms

1) a₁=8, d=5

a) 8,13,18,23,28,33

b) a_n = 8 + 5(n-1) = 3+5n

c) a₂₀ = 3+5(20) = 103

a₅₀ = 3+ 5(50) = 253

2) a₁ = -4, a₂ = -1, d = a₂-a₁ = 3

a) -4,-1, 2,5,8,11

b) a_n = -4 + 3(n-1) = -7+3n

c) a₂₀ = -7+60 = 53

a₅₀ = -7+150 = 143

3) a₃=11, a₄=15, d = 4, a₁= a₃ - 2d = 11 =8 = 3

a) 3,7,11,15,19,23

b) a_n = 3 + 4(n-1) = 3+4n -4 = -1 + 4n

c) a₂₀ = -1 + 80 = 79

a₅₀ = -1 + 200 = 199

4) a₁ = 3, a₁₁ = 58, 58 = 3 + d(11-1), 10d= 55, d= 5.5

a) 3,8.5,14,19.5,25,30.5

b) a_n = 3 + 5.5(n-1) = 3 + 5.5n - 5.5 = -2.5 + 5.5n

c) a₂₀ = -2.5 + 5.5(20) = -2.5 + 110 =107.5

a₅₀ = -2.5 + 5.5(50) = 275-2.5 = 272.5