What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?

Step-by-step explanation:

The nth term of a geometric sequence is expressed as;

Sn = a(r^n - 1)/r - 1

a is the first term of the sequence

r is the common ratio

n is the number of terms

From the sequence;

a = 3

r = -6/3 = 12/-6 = -2

n = 5 (since are looking for the sum of first five terms)

Substitute into the formula;

S5 = 3((-2)^5 - 1)/-2 - 1

S5 = 3(-32-1)/-3

S5 = 3(-33)/-3

S5 = -(-33)

S5 = 33

Hence the sum of the first five terms of the sequence is 33

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5