Question

I need help, arithmetic sequences always mess me up

Answer 1

Missing term of the sequence is 399.

Explanation:

In the given table we will try to find the sequence in terms of y and x parameters.

Since y = 3, 12, 21, 30,......... it's an arithmetic progression then we can represent nth term of this sequence as y = a + (x-1)d where a = first term, x = number of terms and d = common difference.

y = 3 + (x-1)×d = 3 + (x-1)×9 = 3 + 9x -9 = (9x - 6)

Now we have to find the term x = 45 ( 45th term)

By putting the value of x = 45 in the equation we will find the value of y.

y = 9×45 - 6 = 405 -6 = 399

Answer 2

`a_(45)=399` is the required term.

Explanation:

We have been given an arithmetic sequence where we have a common difference which is:
`d=a_2-a_1`

`d=12-3=9`

We will use the formula to find the required term:

`a_n=a+(n-1)d`

where, a is first term which is 3 and d is the common difference which is 9

and n =45 which we require to find.

`a_(45)=3+(45-1)(9)`

`a_(45)=3+396`

`a_(45)=399`.