All categories

2 years ago

Two terms of an arithmetic sequence are a10=16 and a35=66 find the sum of the first 75 terms

1 answer:

4 0

The sum of the first 75 terms of the arithmetic sequence that has 10th term as 16 and the 35th term as 66 is 5400.

<h3>How to find the sum of terms using Arithmetic sequence formula</h3>

aₙ = a + (n - 1)d

where

a = first term

d = common difference

n = number of terms

Therefore, let's find a and d

a₁₀ = a + (10 - 1)d

a₃₅ = a + (35 - 1)d

Hence,

16 = a + 9d

66 = a + 34d

25d = 50

d = 50 / 25

d = 2

16 - 9(2) = a

a = 16 - 18

a = -2

Therefore, let's find the sum of 75 terms of the arithmetic sequence

Sₙ = n / 2 (2a + (n - 1)d)

S₇₅ = 75 / 2 (2(-2) + (75 - 1)2)

S₇₅ = 37.5 (-4 + 148)

S₇₅ = 37.5(144)

S₇₅ = 5400

learn more on arithmetic sequence here: brainly.com/question/1687271

You might be interested in

What is the length of a diagonal of a rectangle with a length of 8 meters and a width of 6 meters

RSB [31]

Answer:

10 m

Step-by-step explanation:

If we draw the diagonal of the rectangle, we form a right triangle where the diagonal is the hypotenuse and the legs are 6 and 8.

This is a well-known Pythagorean triple, which gives the diagonal to be 10 m.

7 0

1 year ago

For X, (3x-40°)=2x-10°)

KATRIN_1 [288]

Hello!

3 x - 40^0 = 2 x - 10^0

3 x - 1 = 2 x - 1

3 x = 2x

3 x - 2 x = 0

Hence, the answer is 0

I hope this helps, and have a nice day!

4 0

3 years ago

I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

5 0

2 years ago

What is the value of 8 in the number 8000

Free_Kalibri [48]

Answer: 8000

Step-by-step explanation:

6 0

2 years ago

Ron has $49.Matt has $19 more than Ron.Naomi has $12 less than Matt.How much money do they have altogether?

EleoNora [17]

The answer to your question is,

They have a total of $173 altogether!

-Mabel <3

5 0

2 years ago

Read 2 more answers