Question

H(n)=−31−7(n−1) complete the recursive formula for h(n)

Answer 1

Answer:

h(1)=-31

h(n)=h(n-1)+(-7)

Step-by-step explanation:

Answer 2

Answer:

h(n+1) = h(n) - 7

Step-by-step explanation:

Our objective is to write the expression for h(n+1) in terms of h(n) which equals -31 -7(n-1)

So we use the given formula to find what h(n+1) is:

h(n+1) = -31 -7((n+1)-1)

h(n+1) = -31 -7(n+1-1)

we now re-arrange the order of terms inside the parenthesis without combining like terms:

h(n+1) = -31 -7(n-1+1)

and use distributive property to multiply "-7" times the "+1" term and get it extracted from inside the parenthesis:

h(n+1) = -31 -7(n-1) -7

Notice that this way we were able to preserve the form of the term h(n) "-31 -7(n-1)" , and see what is the modification introduced to it when finding the term h(n+1). We now replace "-31 -7(n-1)" by "h(n)" in the above equation:

h(n+1) = -31 -7(n-1) -7

h(n+1) = h(n) - 7

And this is the recursive formula that tells us how to construct the following term of a sequence by knowing the previous one.