Question

The sixth term of an arithmetic sequence is 3 2 , and the twelfth term is 5 2 . What is the common difference of the arithmetic sequence? The common difference is .

Answer 1

Answer:

Let "an" denote the n-th term in the sequence. For an arithmetic sequence, there is a constant number added to successive terms:

a7=a6+d

a8=a7+d=a6+2d

a9=a8+d=a6+3d

...

a12=a11+d=a6+6d

We know  a6=3/2 and a12=5/2, so we get

5/2=3/2+6d  6d=1   d=1/6

Answer 2

The sequence has a common difference, and the common difference of the arithmetic sequence is 10/3

How to determine the common difference?

The given parameters are:

T6 = 32

T12 = 52

The nth  term of an arithmetic progression is:

Tn = a + (n - 1) * d

So, we have:

T6 = a + 5d = 32

T12 = a + 11d = 52

Subtract both equations

a - a + 11d - 5d = 52 - 32

Evaluate

6d = 20

Divide both sides by 6

d = 10/3

Hence, the common difference is 10/3

Read more about arithmetic progression at:

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