Find the 14th term of the following geometric sequence.
5, 15, 45, 135, ...

7,971,615

Step-by-step explanation:

A geometric sequence is one in which the successive terms show a regular pattern of change defined by a common ratio i.e the division of the successive term with the previous term gives a constant known as the common ratio.

Where r is the common ratio, a is the first term and n is the number of term, the nth term Tn of a geometric sequence may be defined as

Tn = ar^(n-1)

where a = 5, r = 15/5 = 3

then T14 = 5 * 3(14 - 1)

= 7,971,615

the answer for this question is 38

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