Sequences and Series Part 1

Question

2. Write a recursive definition for the sequence 8, 6, 4, 2, … (1 point)
a_1 = 8; a_n= a_(n–1) − 2
a_1 = 2; a_n= a_(n–1) + 6
a_1 = 8; a_n= a_(n–1) + 2
a_1 = 2; a_n= a_(n–1) + 8

Answer 1

Looks like each term is 2 less than its previous one.
That's the key to the formula

so we have to start with a(1) = 8
then a(n) = a(n-1) - 2 , n>1

the first one matches that.

Answer 2

ty, can you help with this one:
3. Write an explicit formula for the sequence –4, 1, 6, 11,… (1 point)
a_n = –4 + 5(n + 1)
a_n = –4 + 5(n – 1)
a_n = –4 + (n – 1)
a_n = –4 + 5n

Answer 3

The terms are increasing by 5, so I would expect to see something like
a(n) = 5n + ?? , (that rules out #3)
when n = 1, a(1) = 5 + ?? , but that is supposed to be -4
5 + what = -4
what = -9
so a(n) = 5n - 9

I don't see a -9, but what if we expand their expressions

1st: a(n) = -4 + 5(n-1)
= -4 + 5n - 5
= 5n -9
Yeahhh! that's it. So it is the first one