Question

Find the next three terms in the sequence 3/4, 1/2, 1/4, 0​

Answer 1

`\sf \bf (-1)/(4) \ ; \ (-1)/(2) \ ; \ (-3)/(4)`

Explanation:

Arithmetic sequence:

Each term in the arithmetic sequence is obtained by adding or subtracting a common number with the previous term.

To find the next three terms, we need to find the common difference.

Common difference = second term - first term

`\sf = (1)/(2)-(3)/(4)\\\\=(2-3)/(4)\\\\=(-1)/(4)\\\\\\\text{Each term is obtained by adding $(-1)/(4) $ with the previous term}`

Next three terms are,

`\sf 0 + \left((-1)/(4)\right)= 0 - (1)/(4)=(-1)/(4)\\\\\\(-1)/(4)+\left((-1)/(4)\right)=(-1)/(4)-(1)/(4)=(-2)/(4)=(-1)/(2)\\\\\\(-1)/(2)+\left((-1)/(4)\right)=(-1)/(2)-(-1)/(4)=(-2-1)/(4)=(-3)/(4)`