Find the 8th term of the geometric sequence 7,−21,63,

8th term is -15309

Step-by-step explanation:

r is the common difference, r = -21/7 = -3

a₈ = - 15309

Step-by-step explanation:

The nth term of a geometric sequence is

= a₁

where a₁ is the first term and r the common ratio

Here a₁ = 7 and r = = = - 3 , then

a₈ = 7 × = 7 × - 2187 = - 15309

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions