The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 462, 453,444,...

Find the 32nd term.

183

Explanation:

462, 453, 444

Always start by subtracting the consecutive numbers.

462 - 453 = 9

453 - 444 = 9

Normally you can see a patron, and here there his is no exception :-).

You can construct the next number by subtracting 9 of the previous number in the sequence.

462 - 9

453 - 9

444 - 9

435 and so on...

If you want to find the 4th term then you need to multiply the 3rd by 9 and subtract it from the first term.

When you start with 462 - (3*9) you get 462 - (27) = 435

The same goes for the 32 term...

When you start with 462 - (31*9) you get 462 - (279) = 183

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for