Determine the next three terms in the following sequence: 2, 3, 5, 8,a. 13, 19, 26 b. 12, 17, 23 c. 12, 16, 20 d. 13, 17, 23

The correct option is b.

Step-by-step explanation:

The given sequence is

2, 3, 5, 8, ____, ____, ____,.

The first term is 2, second term is 3, third term is 5 and fourth term is 8.

Form the above equation it is clear that the recursive formula for  the given series is

where, .

Substitute n=5 to find 5th term,

Substitute n=6 to find 6th term,

Substitute n=5 to find 7th term,

The next three terms are 12, 17, 23. Therefore the correct option is b.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)