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

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.

h (1) = -31

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