Consider the sequence of numbers 50, 48, 46, 44, using n to represent a position of a number in this sequence, write an expression that allows you to calculate the nth number

The given sequence is

Here the first term, a is 50.

And the difference between two consecutive terms are

So the difference is constant, which is -2. Therefore the sequence is arithmetic .

And the nth term of aritmnetic series is given by

Substituting the values of a and d, we will get

, 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