Question

1. in a particular sequence, you multiply the term number by 6 and subtract 3, to determine a particular term.

a) determine the sixth term.
b) which term is 63?

Explanation:

Step1: Define the sequence formula

Let $n$ = term number, term value $a_n = 6n - 3$

Step2: Calculate 6th term (part a)

Substitute $n=6$ into formula:
$a_6 = 6(6) - 3$
$a_6 = 36 - 3 = 33$

Step3: Solve for $n$ when $a_n=63$ (part b)

Set $6n - 3 = 63$, solve for $n$:
$6n = 63 + 3 = 66$
$n = \frac{66}{6} = 11$

Answer:

a) 33
b) 11th term