Question

What is the recursive formula for this sequence?

14, 18, 22, 26, 30, ...

A {a1 = 34
{an = an-1+4

B {a1 = 14
{an = an-1 -4

C {a1 = 14
{an = an-1 + 4

D {a1 = 4
{an = an-1 + 14

Answer 1

The recursive formula for the sequence 14, 18, 22, 26, 30, ... is 'a1 = 14' and 'an = an-1 + 4', which reflects that each term is 4 more than the previous one. Option C is the correct answer.

Step-by-step explanation:

The student asked for the recursive formula for the sequence 14, 18, 22, 26, 30, ... To determine the recursive formula, we must identify the pattern of the sequence. By observing the sequence, we notice that each term is 4 more than the previous term. Therefore, the recursive formula should reflect this by adding 4 to the previous term (an-1).

The correct recursive formula is given by:

• a1 = 14
• an = an-1 + 4

This pattern can be applied to find any term in the sequence by starting at the first term (a1 = 14) and adding 4 repeatedly to get subsequent terms. Hence, the correct option is: C:

{a1 = 14

{an = an-1 + 4