Find the sum of the first 10 terms.
8,20,32,44...

8,20,32,44,56,68,80,92,104,116,128

Step-by-step explanation

Just keep adding 12

620

Step-by-step explanation:

This is a progression but we need to find out whether it is Arithmetic Progression or an exponential or geometric progression.

From the quest, 8, 20, 32, 44, this is not an exponential function but an arithmetic progression because, when you subtract the first time from the second term , the common difference is 12.

20 - 8 = 12, so this is an arithmetic progression as said earlier. Now to find the sum of the first ten terms of the series, we apply the formula which is

S10 = n/2{(2a + ( n - 1 )d}, where n = 10, and a = 8 the first term and d the common difference = 12.. Now substitute for the values

S10 = 10/2{(2 x 8 + ( 10 - 1 )12}

= 5( 16 + 9 x 12)

= 5( 16 + 108 )

= 5( 124 )

= 620.

Therefore, the sum of the 10 terms of the series is 620.

But we can also solve it using other means . To solve this we first find the last term which is the 10th term using this formula

T10 = a + ( n - 1 )d

= 8 + (10 -1)12

= 8 + 9 x 12

= 8 + 108

= 116.

Now with this we could put this in the equation below.

S10 = n/2( a + L ) where L is the last term calculated above. Now we substitute to get the sum.

S10 = 10/2( 8 + 116)

= 5( 8 + 116 )

= 5( 124)

= 620.

I could have explained how we arrived at the formula above but the time could not permit, I will discuss that in the next lecture if I come across such question.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!