The first two terms of an arithmetic series are -2 and 3. How many terms
needed for the Sum to be 306?
​

Number of term n = 12

Step-by-step explanation:

Given:

a1 = -2

a2 = 3

Sum = 306

Find:

Number of term n

Computation:

d = a2 - a1

d = 3 - (-2)

d = 5

Sn = n/2[2a + (n-1)d]

306 = n/2[2(-2) + (n-1)5]

612 = n[-4 + 5n -5]

5n² - 9n - 612 = 0

Number of term n = 12

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180