Answer:
a, n(n) = n(1) - 3 x (n - 1)
b, n(n) = n(1) - 5 x (n - 1)
Step-by-step explanation:
We will define the 1st term.
Then we represent all other terms in the form of 1st term and n.
Both sequences are solved in same way.
a,
1st term: n(1) = 4
2nd term: n(2) = 1 = 4 - 3 = n(1) - 3 x 1 = n(1) - 3 x (2 - 1)
3rd term: n(3) = -2 = 4 - 6 = n(1) - 3 x 2 = n(1) - 3 x (3 - 1)
4th term: n(4) = -5 = 4 - 9 = n(1) - 3 x 3 = n(1) - 3 x (4 - 1)
5th term: n(5) = -8 = 4 - 12 = n(1) - 3 x 4= n(1) - 3 x (5 - 1)
...
nth term: n(n) = n(1) - 3 x (n - 1)
b,
1st term: n(1) = -7
2nd term: n(2) = -12 = -7 - 5 = n(1) - 5 x 1 = n(1) - 5 x (2 - 1)
3rd term: n(3) = -17 = -7 - 10 = n(1) - 5 x 2 = n(1) - 5 x (3 - 1)
4th term: n(4) = -22 = -7 - 15 = n(1) - 5 x 3 = n(1) - 5 x (4 - 1)
5th term: n(5) = -27 = -7 - 20 = n(1) - 5 x 4 = n(1) - 5 x (5 - 1)
...
nth term: n(n) = n(1) - 5 x (n - 1)
Hope this helps!
