Answer:
3. aₙ = -9n +7
4. d = -2.4
5. a₆ = 45
6. aₙ = 133 + 4n
Step-by-step explanation:
Question 3.
a₁ = -2; aₙ = aₙ₋₁ - 9
The explicit rule for an arithmetic sequence is
aₙ = a₁ + d(n -1 )
d = aₙ - aₙ₋₁
aₙ = aₙ₋₁ - 9 Subtract aₙ₋₁ from each side
aₙ - aₙ₋₁ = -9
d = -9
For this sequence,
aₙ = -2 – 9(n - 1) Remove parentheses
aₙ = -2 - 9n + 9 Combine like terms
aₙ = -9n + 7
===============
Question 4
d = aₙ - aₙ₋₁
a₂ - a₁ = 6.2 – 8.6 = -2.4
a₃ - a₂ = 3.8 – 6.2 = -2.4, etc.
The common difference is
d = -2.4
===============
Question 5
aₙ = 8n – 3 Substitute the value of n
a₆ = 8×6 – 3
a₆ = 48 - 3
a₆ = 45
============
Question 6
a₁ = 137; d = 4
aₙ = a₁ + d(n -1 )
aₙ = 137 + 4(n -1 )
aₙ = 137 + 4n -4
aₙ = 133 + 4n
