what is the 33rd term of the arithmetic sequence 9.4, 10.6, 11.8, 13,...?

Answer 1

what is the 33rd term of the arithmetic sequence 9.4, 10.6, 11.8, 13,...?

Seems like you are adding the number 1.2 to the previous term to find the next. This pattern is also consistent. Also notice this pattern.

To find the 2nd term, you add 1.2 ONE time to 9.4 and get 10.6

To find the 3rd term you add 1.2 TWO times to 9.4 and get 11.8

To find the 4th terms you add 1.2 THREE times to 9.4 and get 13.0

Notice the pattern??

To find the 33rd term, you add 1.2 _______ to 9.4 and get ________t

Answer: Add 1.2 thirty-times (33 - 1 = 32) based on the pattern and you get: 47.8

Answer 2

Arithmetic sequences are similar to linear equations. Linear equations have a constant slope, or rate of change. Arithmetic sequences have a common difference, the number that is added or subtracted from term to term.

The formula for arithmetic sequences is:

a_n = a₁ + (n-1)d

where a₁ is the first term, n is the number of terms, d is the common difference, and a_n is the nth term, or the term you are trying to find.

For this problem:

a₁ = 9.4

n= 33

d = 1.2

We find the common difference by subtracting a₁ from a₂.

10.6 - 9.4 = 1.2

We are looking for a₃₃.

Then we just plug everything in and solve:

a₃₃ = 9.4 + (33-1)(1.2)

a₃₃ = 47.8