Question

Find the common difference and the next three terms of the arithmetic sequence. 1/4,1/2,3/4,1,5/4

Answer 1

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Answer:

`\large\boxed {(1)/(4)}` Common difference

`\large\boxed{(3)/(2), (7)/(4), 2}` Next three terms

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Find the common difference by subtracting the previous term from a term. We can use the terms 1/4 and 1/2:

Convert 1/2 into a fraction over 4:

1/2 · 2/2 = 2/4

Find the common difference by subtracting the fractions:

2/4 - 1/4 = 1/4. This is the common difference.

Find the next 3 terms by adding 1/4:

5/4 + 1/4 = 6/4 (Reduce fraction) = 3/2

6/4 + 1/4 = 7/4

7/4 + 1/4 = 8/4 (Reduce fraction)

Therefore, the next 3 terms are 3/2, 7/4 and 2.