Question

Write an explicit formula for the sequence -13, -6, 1, 8, ...

a) an = -13n+7
b) an = -13+(n+7)
c) an = -13+7(n-1)
d) an = -13n+7

Answer 1

The answer is:

c)
`a_(n)=-13+7(n-1)`

Answer 2

c) an = -13+7(n-1)

Explanation:

We can use the formula for arithmetic sequences

an =a1+d(n-1)

where a1 is the first term in the sequence

d is the common difference

and n is the term number

a1 is -13

d is found by taking the second term and subtracting the first term

d = -6--13

= -6+13

d=7

We are adding 7 each time

Substituting what we know,

an = -13 + 7(n-1)