Common Ratio / Difference (Level 1)

Question

Question
Find the common difference of the arithmetic sequence.
4,12,20, ...

Answer 1

The common difference is found by subtracting the second term from the first term in the sequence.

12 - 4 = 8

Therefore, the common difference in the arithmetic sequence 4,12,20, ... is 8.

Answer 2

Nth Term of an Arithmetic Sequence
Question
Find the 94th term of the arithmetic sequence.
−26,−37,−48, ...

Answer 3

To find the nth term of an arithmetic sequence, we can use the formula:

nth term = a + (n-1)d

where:
- a is the first term in the sequence
- n is the position of the term we want to find
- d is the common difference between terms

Given the sequence: -26, -37, -48, ...
The first term: a = -26
The common difference: d = -37 - (-26) = -37 + 26 = -11

Now, we want to find the 94th term:
n = 94

Plugging into the formula:
94th term = -26 + (94-1)(-11)
94th term = -26 + 93(-11)
94th term = -26 - 1023
94th term = -1049

Therefore, the 94th term of the arithmetic sequence -26, -37, -48, ... is -1049.