Question

the first five terms of a sequence are 7,10,13,16, and 19. Which of the following functions define this sequence for all the integers n>1

Answer 1

The first five terms of a sequence are 7,10, 13 , 16 and 19. which of the following functions define this sequence for all integers n>or equal to 1?

A. f[n]= 3n=7

B.f[n]= 4+3n

C. f[n]= 4[3]^n-1

D.f[n]=7[3]^n-1

Answer:

Option B is correct.

`f(n)=4+3n`

Explanation:

Given:

The given sequence of an AP is.

7,10,13,16,19......

The first term of an AP
`a=7`

And common difference
`d=10-7=3`

The function which defined this sequence is;

`f(n)=a_(n)=a+(n-1)d`

Now we substitute a and d value in above equation.

`f(n)=7+(n-1)3`

`f(n)=7+3n-3`

`f(n)=4+3n`

therefore, the function for the given sequence for all integers
`n\geq 1` 1 is;
`f(n)=4+3n`