Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) {1, 7, 13, 19, 25, . . . }

the formula is a_n = 6n - 5

Step-by-step explanation:

The formula is

Given that

{1, 7, 13, 19, 25, . . . }

The difference between the numbers is

7 -  1 = 6

13 -7 = 6

19 - 13 = 6

a = 1

d = 6

Now the formula is

a_n = a + (n - 1)d

= 1 + (n - 1)6

= 1 + 6n - 6

= 6n - 5

So, the formula is a_n = 6n - 5

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

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step-by-step explanation:

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