Answer:
a) common difference = 5
b) common difference = - 2
c) not an arithmetic sequence
last question:
nth term: aₙ = 3n - 1
a₅₀ = 149
a₄₀₀ = 899
Explanation:
Common difference d = difference between successive terms
For a)
d = 9 -4 = 14 - 9 = 5
For b)
d = 8 - 10 = 6 - 8 = -2
For c) 5, 5, 2, 0
5 -5 = 0
which is not equal to
2 - 5 = 3
So this is not an arithmetic sequence
(unless of course the series numbers have been copied wrong)
For the last question
Sequence = 2, 5, 8, 11, 14, ...
d = 5 - 2 = 8 -5 = 3
The nth term of an arithmetic sequence is given by the formula:
aₙ = a₁ + d(n-1)
where a₁ = first term = 2
d = 3
So
aₙ = 2 + 3(n- 1)
aₙ = 2 + 3n - 3
aₙ = 2 -3 + 3n
aₙ = -1 + 3n
aₙ = 3n - 1
Check:
a₂ = 3(2) - 1 = 5
a₃ = 3(3) - 1 = 8
a₄ = 3(4) - 1 = 11
a₅₀ = 3(50) - 1 = 150 - 1 = 149
a₃₀₀ = 3(300) - 1 = 900 - 1 = 899