Give the next three terms and both the explicit and recursive formula for 25, 23, 19, 11

The question really does depend on getting the explicit formula.

Explicit

t1 = 25

t2 = 23 The difference is 2 to get to 25

t3 = 19 which means that you need 6 to get back to 25

t3 = 25 - 2*3

t3 = 25 - 2*(2^(n-1) - 1)

t3 = 25 - 2*(2^(2) - 1 )

t4 = 11 which means that you need 14 to get back to 25

t4 = 25 - 2*7

t4 = 25 - 2*(2^3 - 1)

t5 = 25 - 2*(2^4 - 1)

t5 = 25 - 2*(16 - 1)

t5 = 25 - 2*15

t5 = - 5

tn = 25 - 2*(2^(n- 1) - 1)     Explicit  Answer

Recursive

t1 = 25

t2 = 23 which is t1 - 2^(n-1)

t3 = t2 - 2^(n - 1)

t3 = 23 - 2^(3 - 1)

t3 = 23 - 2^2

t3 = 23 - 4

t3 = 19

The recursive formula is

tn = t_(n -1) - 2^(n - 1)   Answer Recursive.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.