Answer:
The Recursive Formula of sequence is: 8, 5, 2, -1, -4,...
Step-by-step explanation:
Arithmetic Sequence is a sequence in which every two neighbor digits have equal distances.
For finding the nth term, we use formula
aₙ = a + (n - 1) d
where, aₙ = value of nth term
a = First term
n = number of term
d = difference
We have given that,
a₁₇ = -40 ⇒ a₁₇ = a + (17 - 1)d
⇒ -40 = a + 16d → (1)
Also, a₂₈ = -73 ⇒ a₂₈ = a + (28 - 1)d
⇒ -73 = a + 27d → (2)
Solving, equation (1) and (2), We get
a = 8, d = -3
Hence, First term = a = 8
Second term = a + d = 8 - 3 = 5
Third term = 5 + d = 2
Fourth term = 2 + d = -1
Thus, The Arithmetic Sequence is: 8, 5, 2, -1, -4,...
