The sum of the first

6

66 terms of a geometric series is

15

,

624

15,62415, comma, 624 and the common ratio is

5

55.

What is the first term of the series?

The first term of the series is 4

Step-by-step explanation:

The sum of the first  6  terms of a geometric series is  15 , 624  and the common ratio is  5 .

To find the first term, we use the formula for the sum of terms in a geometric series.

Since the common ratio of the series is greater than 1, the sum of term of the geometric series is;

where r = common ratio

a = first term

When S = 15,624, r = 5 and n = 6, the first term, a, will be:

a = 4

The first term of the series is 4.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15