Question

In this arithmetic sequence,the difference between each pair of consecutive terms is 1/2. Find the next term in the sequence. Express your answer in lowest terms. 1/5,7/10,1 1/5

Answer 1

You have a arithmetic sequence, it means that the difference between each term is the same, in this case the difference is 1/2.

`(1)/(5),(7)/(10),1,(1)/(5),\ldots`

Then to find the next term you have to add 1/2 to the last term you have:

`(1)/(5)+(1)/(2)`

To add fractions with different denominator you follow the next formula:

`(a)/(b)+(c)/(d)=(a\cdot d+b\cdot c)/(b\cdot d)`

Then you get: