Question

The explicit rule for a sequence is given. Find the position number of the term 62.

f(n) = (2n - 2) + 2

Answer 1

The explicit rule for the sequence is given by \( f(n) = (2n - 2) + 2 \). To find the position number (\( n \)) of the term 62, set \( f(n) \) equal to 62 and solve for \( n \):

\[ (2n - 2) + 2 = 62 \]

Combine like terms:

\[ 2n = 62 - 2 \]

\[ 2n = 60 \]

Divide by 2:

\[ n = 30 \]

So, the term 62 is at position number 30 in the sequence.

Answer 2

To find the position number of the term 62 in the sequence with the explicit rule f(n) = (2n - 2) + 2, solve the equation (2n - 2) + 2 = 62 for n. The solution is n = 30, so the position number of the term 62 is 30.

Step-by-step explanation:

To find the position number of the term 62 in the sequence with the explicit rule f(n) = (2n - 2) + 2, we need to solve the equation for n. The explicit rule gives us the formula for the nth term, so we can set it equal to 62 and solve for n. Here's how:

(2n - 2) + 2 = 62

2n = 62 - 2

2n = 60

n = 30

Therefore, the position number of the term 62 is 30.