Question

The third term in a sequence is 16.

The term-to-term rule is "add 5".
Write an expression, in terms of n, for the nth term of the sequence.

Answer 1

To express the nth term of a sequence where the third term is 16 and the rule is to 'add 5', we calculate backward to find the first term as 6. Then we create a formula for the nth term: Tn = 5n + 1.

Step-by-step explanation:

To find an expression, in terms of n, for the nth term of a sequence where the third term is 16 and the term-to-term rule is "add 5", we can work backwards to find the first term.

Starting with the third term (which is when n=3):

3rd term = 16

2nd term = 3rd term - 5 = 16 - 5 = 11

1st term = 2nd term - 5 = 11 - 5 = 6

Therefore, the first term when n=1 is 6. The rule "add 5" indicates that each term increases by 5 from the previous term. So to get from the first term to the nth term, we add 5 (n-1) times.

The nth term, Tn, can be expressed as:

Tn = first term + 5 * (n - 1)

Substitute the value of the first term (6) into the equation:

Tn = 6 + 5 * (n - 1)

Which simplifies to:

Tn = 5n + 1

Answer 2

s(n) = (5n) + 1

Step-by-step explanation:

s(n) = (5n) + 1 when n = 3 s(3) = 16

term to term is 5 more than the previous term "add 5"