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 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 1

Answer:

Option B is correct

For $n\geq 1$ , the function for the given sequence is defined as; $f[n] = 4 +3n$

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.

An explicit formula for this arithmetic sequence given by;

$a_n = a+(n-1)d$ where a represents first term

Since, the given sequences; 7 , 10 , 13 , 16 and 19

⇒ common difference(d) = 3 and a = 7

Since.

10 -7 = 3

13- 10 = 3  ....

The function which defined this sequence is;

$f[n]=a_n = 7 +(n-1)(3)$

using distributive property:

$f[n] = 7 + 3n -3$

$f[n] = 4 +3n$

therefore, the function for the given sequence for all integers $n\geq 1$ is;  $f[n] = 4 +3n$