Find an explicit formula for the arithmetic sequence -5, 13, 31, 49,.

Note: the first term should be b(1).

B(n)=(blank)

b(n) = -23 + 18n

Step-by-step explanation:

NOTE - This is an arithmetic sequence, so each number is increasing by addition. If you were in a geometric sequence, however, you'd be multiplying. This means that the explicit formula for the geometric sequence you'll be learning later on will be different.

The formula for explicit formula is b(n)=b(1)+d(n-1). The variable d represents the common difference and the a is whatever number of the term you are using.

Since you have b(1), you look at what your first term is. Plug -5 into a(1).

To find your common difference, find 13-(-5). This is 18, and adding it to the others you can see that it continues.

So, plugging in what you have so far it looks like b(n) = -5 + 18(n - 1)

All we need to do now is simplify.

1. Distribute: -5 + 18n - 18

2. Add like terms: -23 + 18n

Hope this helped and made sense lol.

-1/2 +2

step-by-step explanation:

, 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