Math

QuestionDetermine the common difference in the arithmetic sequence 11,20,29,11, 20, 29, \ldots

Studdy Solution

STEP 1

Assumptions1. The given sequence is an arithmetic sequence. The first few terms of the sequence are11,20,293. The common difference is the same between each consecutive pair of terms

STEP 2

In an arithmetic sequence, the common difference is found by subtracting any term from the term that follows it. Let's denote the common difference as dd, and the terms as a1,a2,a,a1, a2, a, \ldots where a1a1 is the first term, a2a2 is the second term, and so on.
d=a2a1d = a2 - a1

STEP 3

Now, plug in the given values for a1a1 and a2a2 to calculate the common difference.
d=2011d =20 -11

STEP 4

Calculate the common difference.
d=2011=9d =20 -11 =9

STEP 5

To confirm that this is indeed the common difference, let's check it with the next pair of terms.
d=a3a2d = a3 - a2

STEP 6

Again, plug in the given values for a2a2 and a3a3.
d=2920d =29 -20

STEP 7

Calculate the common difference again.
d=2920=9d =29 -20 =9Since the common difference is the same for both pairs of terms, we can conclude that the common difference of the arithmetic sequence is9.

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