For some number, t, the first 3 terms of an arithmetic sequence are
t + 2, 3t, 4t + 1
Which of the following is the numerical value of the 4th
term.

a₄ = 17

Step-by-step explanation:

The difference d between consecutive terms of an arithmetic sequence are constant, that is

a₂ - a₁ = a₃ - a₂, substituting values

3t - t - 2 = 4t + 1 - 3t

2t - 2 = t + 1 ( subtract t from both sides )

t - 2 = 1 ( add 2 to both sides )

t = 3

Thus

a₁ = t + 2 = 3 + 2 = 5

a₂ = 3t = 3(3) = 9

a₃ = 4t + 1 = 4(3) + 1 = 12 + 1 = 13

The first 3 terms of the sequence are

5, 9, 13 with

d = 9 - 5 = 13 - 9 = 4 , thus

a₄ = 13 + 4 = 17

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.