What is the term of a 7-term geometric series if the first term is -11 the last term is -45,056 and the common ratio is -4

1 answer:

8 0

I assume you mean to ask how to find the sum of the seven terms?

You have

$a_2=ra_1$
$a_3=ra_2=r^2a_1$
$a_4=ra_3=r^3a_1$
...
$a_7=ra_6=r^6a_1$

So the sum is

$a_1+ra_1+r^2a_1+\cdots+r^6a_1=a_1(1+r+r^2+\cdots+r^6)=a_1\times\dfrac{1-r^7}{1-r}$

You know that $a_1=-11$ and $r=-4$ , so the sum is equal to

$-4\times\dfrac{1-(-4)^7}{1-(-4)}=-13108$

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Read 2 more answers

Graph the function y = x3 + 3x2 – x – 3. Which lists all of the turning points of the graph? (–3, 0) and (1, 0) (–2, 3) and (0,

Vlada [557]

Answer with explanation:

The given function is:

y=x³+3 x²-x-3

=x²(x+3) -1(x+3)

= (x²-1)(x+3)

= (x-1)(x+1)(x+3)

Put, y=0 , gives

⇒ (x-1)(x+1)(x+3)=0

≡→x-1=0 ∧ → x+1=0 ∧→x+3=0

≡x=1, -1, -3

So, there are three breaking points in the curve.

1.⇒Putting, x=1 , in the function

y(1)=1³+3×1²-1 -3

=1 +3-4

2. ⇒Putting, x=-1 , in the function

y(-1)=(-1)³+3×(-1)²-(-1) -3

= -1 +3+1-3

3.⇒Putting, x=-3 , in the function

y(-3)=(-3)³+3×(-3)²-(-3) -3

=-27+27+3-3

So, These are points where curve crosses the X axis, which are , (1,0),(-1,0) and (-3,0).

But turning points are those points where curve takes the turn , that is, if it is increasing function then it starts decreasing or becomes constant function after that point, and if it is a decreasing function then it becomes increasing or constant function.

So,turning points of the given function by looking at the graph of the function by approximation

Option B:→(-2,3) and (0, -3)