Question

Write the equation for the linear function in both explicit and recursive formsy= x +f(0) =f(x) = f(x-1)7. 2,4, 6, 8, 10.......8. 11, 12, 13, 14 15,16....9. 15. 15.5, 16, 16.5, 17, 17.5 ....10. 12, 8, 4, 0, -4, -8......11

Answer 1

For the sequence 2, 4, 6, 8, 10......

You can observe that the common difference is 2

`T_2-T_1\text{ = 4 - 2 = 2}`
`f(0)\text{ = 2}`

Since we already know that the common difference is 2, the recursive formula can be written generally as :

`f(x)\text{ = }f(x-1)\text{ + 2}`

Where f(x) is the present term and f(x-1) is the preceding term

The equation written above is the linear equation in the recursive form.

For the explicit form of the linear equation

Since the common difference, d = 2. It is obvious that the equation is an AP

The general formula for an arithmetic progression is:

`T_n\text{ = }a\text{ + (n - 1)d}`

The first value, a = 2

The common diference, d = 2

The explicit form of the linear equation then becomes:

`T_n=\text{ }2\text{ + }(n\text{ - 1) }2`

Where n is the number of terms in the sequence