All categories

3 years ago

How many terms of the ap 9,17,25,...... must be taken to get a sum of 450

Mathematics

1 answer:

dalvyx [7]3 years ago

7 0

The AP is 9, 17, 25,.......

a (first term) = 9

d (common difference) = 17-9 = 8

Let n be the required number of terms.

Sn (sum of the n terms) = 450

We know that Sn = n/2 (2a + (n-1)d )

450 = n/2 (18 + (n-1)8 )

900 = n(18 + 8n -8)

900 = 8n2 + 10n

8n2 + 10n -900 = 0

8n2 +80n -90n -900 = 0<span>
</span>

8n (n +10) -90 (n- 10) = 0

(n-10)(8n-90) = 0

n = 10 or 11.25

But n has to be a natural, since number of terms is always a natural number.

Thus, the required number of terms is 10.

You might be interested in

A square cake is cut into 16 equal parts.

faust18 [17]

So 4 times 4 is 16 so the 1/4 is now 4/16 plus the 7/16 equals 11/16 so the left number is 5/16

8 0

3 years ago

Read 2 more answers

Carina begins to solve the equation -4 - 2/3x = -6 by adding 4 to both sides. Which statements regarding the rest of the solving

Andru [333]

Answer:

A.) After adding 4 to both sides, the equation is $-\frac{2}{3}x=-2$

C.) The equation can be solved for x using exactly one more step by multiplying both sides by $-\frac{3}{2}$

D.) The equation can be solved for x using exactly one more step by dividing both sides by $-\frac{2}{3}$

Step-by-step explanation:

The correct questions is as follows:

Carina begins to solve the equation -4-2/3x=-6 by adding 4 to both sides. Which statements regarding the rest of the solving process could be true? Check all that apply.

A.) After adding 4 to both sides, the equation is -2/3x=-2.

B.) After adding 4 to both sides, the equation is -2/3x=-10 .

C.) The equation can be solved for x using exactly one more step by multiplying both sides by -3/2.

D.) The equation can be solved for x using exactly one more step by dividing both sides by -2/3.

E.) The equation can be solved for x using exactly one more step by multiplying both sides by -2/3.

Given equation:

$-4-\frac{2}{3}x=-6$

To show the steps we will carry out in order to solve for $x$

Solution:

Solving for $x$

Step 1:

Adding both sides by 4

$4-4-\frac{2}{3}x=-6+4$

Thus, we get:

$-\frac{2}{3}x=-2$

Thus statement A is correct.

Step 2:

Multiplying both sides by $-\frac{3}{2}$

$-\frac{3}{2}\times -\frac{2}{3}x=-2\times -\frac{3}{2}$

Thus, we get:

$x=3$ [Two negatives multiply to give a positive]

This proves that statement C is correct.

Or Step 2:

Dividing both sides by $-\frac{2}{3}$

$\frac{-\frac{2}{3}x}{-\frac{2}{3}}=\frac{-2}{-\frac{2}{3}}$

Thus, we get:

$x=-2\times -\frac{3}{2}$ [On dividing with a fractional divisor, we take reciprocal and multiply it with the dividend.]

$x=3$ [Two negatives multiply to give a positive]

This prove that statement D is correct.

5 0

3 years ago

How many milliliters are equal to 7 liters?

AlekseyPX

Answer:

7000

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

I dont understand the math can pls help

Vera_Pavlovna [14]

Answer: 46.7 in/3

Step-by-step explanation:

7 0

2 years ago

Draw a circle with center A and a radius of your choice. Create three well-spaced points, B, C, and D, on the circle in clockwis

Dmitry [639]

Answer:

Please find attached the required circle

It is observed that the angle subtended by the arc CB which are m∠CAB and m∠CDB is such that the angle arc CB subtends at the center, m∠CAB is two times the angle that the arc CB subtends at the circumference

The measured angle subtended by the arc CB at the center m∠CAB = 64° and the measured angle subtended by the arc CB at the circumference m∠CDB = 32°

Step-by-step explanation:

5 0

3 years ago