Question

nth term
A sequence of numbers is shown: 2, 9, 16, 23, 30 ... ...
(a) Find an expression for the nth term of the sequence.
(b) Find the 100th term in the sequence.
Please help!! Thanks for your answers. Much appreciated for your help.

Answer 1

So, we have a common difference of 7 (9 - 2 = 16 - 9 is true)
For an arithmetic sequence, we have a generalised form:

$a_n = a_1 + (n - 1)d$, where $a_1$ is the first term, n is the nth place, and d is the common difference.

Now, to find the nth term, we substitute n as n to get:

$a_n = 2 + 7(n - 1)$

Hence, to find the 100th term, we substitute n as 100 to get:

$a_100 = 2 + 7(100 - 1)$
$= 2 + 7(99)$
$= 2 + 693$
$= 695$

Thus, the 100th term is 695.