The first term of a geometeic series is 1, the common ratio is 2, and the sum of the series is 63. how many terms are there in this geonetric series?

6 terms

Step-by-step explanation:

To find the number of terms we will use the formula:

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

where a is the first term= 1

r is the common ratio = 2

Sn is the sum of series = 63

n is the number of terms = ?

Now substitute the values in the formula:

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

63= 1(1-2^n)/1-2

63=1(1-2^n)/-1

63*-1 = 1(1-2^n)

-63 = 1-2^n

Now combine the constants:

-63-1= -2^n

-64= -2^n

64= 2^n

2^6 = 2^n

When the base are same powers are equal to each other.

6=n

Thus there are 6 terms

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.