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.
