F(n)=5\cdot(-2)^{\large{\,n-1}}f(n) =5⋅(−2)
n−1
f, left parenthesis, n, right parenthesis, equals, 5, dot, left parenthesis, minus, 2, right parenthesis, start superscript, n, minus, 1, end superscript
Complete the recursive formula of f(n)f(n)f, left parenthesis, n, right parenthesis.
f(1)=f(1)=f, left parenthesis, 1, right parenthesis, equals
f(n)=f(n-1)\cdotf(n)=f(n−1)⋅f, left parenthesis, n, right parenthesis, equals, f, left parenthesis, n, minus, 1, right parenthesis, dot

This does not make sense

This is what i found “an explicit formula designates the nth term of the sequence, as an expression of n (where n = the term's location). it defines the sequence as a formula in terms of n. this example is an arithmetic sequence(the same number, 5, is added to each term to get to the next term).” i hope this you for what your looking for. can you plz mark me brainliest?

The american colonies would have been ruled by a king.

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt