In an arithmetic sequence, the first term is 4, the fourth term is 19, and the nth term is 99. find the common difference and the number of terms n

common difference=5

number of term(n)=20

Step-by-step explanation:

a=4,

but T_{4} =19= a+3d

a+3d=19

4+3d=19

3d=19-4

3d=15

d=15/3

d=5

=a+(n-1)d

99=a+(n-1)d

99=4+(n-1)*5

99=4+5n-5

99=5n-1

5n-1=99

5n=99+1

5n=100

n=100/5

n=20

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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