What is a10 for the sequence (an) = 1 + 3 (n - 1)? i go 28 is that correct?

Question

What is a10 for the sequence (an) = 1 + 3 (n - 1)? i go 28 is that correct?

What is a7 for the sequence an = 2 + 5(n - 1)? i got 51 is that right

6x+7/5 = x, how do i find x?

30-x/10 = 2, what's the next step in solving this equation?

Answer 1

To find the value of a10 for the sequence (an) = 1 + 3(n - 1), you can substitute n = 10 into the formula.

a10 = 1 + 3(10 - 1) = 1 + 3(9) = 1 + 27 = 28

So, your answer of a10 = 28 is correct.

Similarly, to find a7 for the sequence an = 2 + 5(n - 1), substitute n = 7 into the formula.

a7 = 2 + 5(7 - 1) = 2 + 5(6) = 2 + 30 = 32

So, the correct value of a7 is 32, not 51.

To solve the equation 6x + 7/5 = x, you'll need to isolate x.

Start by subtracting x from both sides of the equation:

6x - x + 7/5 = 0

Combining like terms:

5x + 7/5 = 0

Next, subtract 7/5 from both sides:

5x + 7/5 - 7/5 = 0 - 7/5

Simplifying:

5x = -7/5

Finally, divide both sides by 5 to solve for x:

5x/5 = -7/5 ÷ 5

x = -7/25

Therefore, x = -7/25.

To continue solving the equation (30 - x)/10 = 2, you'll need to isolate x.

Start by multiplying both sides of the equation by 10:

10 * (30 - x)/10 = 2 * 10

This simplifies to:

30 - x = 20

Next, subtract 30 from both sides:

30 - x - 30 = 20 - 30

This simplifies to:

-x = -10

Lastly, multiply both sides by -1 to solve for x:

(-1) * (-x) = (-1) * (-10)

This simplifies to:

x = 10

Therefore, x = 10.

Answer 2

To find the value of a10 for the sequence (an) = 1 + 3 (n - 1), you need to substitute the value of n as 10 into the given formula and solve for an. Let's go step by step:

1. Substitute n = 10 into the formula: an = 1 + 3 (10 - 1)
2. Simplify inside the parentheses: an = 1 + 3 (9)
3. Perform the multiplication: an = 1 + 27
4. Add the numbers: an = 28

So, the value of a10 for the sequence is indeed 28, which means you got it correct.

For the second question, to find a7 for the sequence an = 2 + 5(n - 1), follow the same process:

1. Substitute n = 7 into the formula: an = 2 + 5(7 - 1)
2. Simplify inside the parentheses: an = 2 + 5(6)
3. Perform the multiplication: an = 2 + 30
4. Add the numbers: an = 32

Therefore, the value of a7 for the sequence is 32, not 51.

Moving on to the equation 6x + 7/5 = x, to find the value of x, you can follow these steps:

1. Start by subtracting x from both sides of the equation to isolate the term with x: 6x - x + 7/5 = 0.
2. Combine the x terms on the left side: 5x + 7/5 = 0.
3. Next, subtract 7/5 from both sides of the equation to eliminate the constant term: 5x = -7/5.
4. Finally, to solve for x, divide both sides of the equation by 5: x = -7/5 * 1/5 = -7/25.

So, the solution to the equation 6x + 7/5 = x is x = -7/25.

Moving on to the equation 30 - x/10 = 2, the next step in solving this equation would be:

1. Start by isolating the term with x by subtracting 30 from both sides of the equation: 30 - x/10 - 30 = 2 - 30.
2. Simplify the left side: -x/10 = -28.
3. Multiply both sides of the equation by -10 to eliminate the fraction: -10 * (-x/10) = -10 * (-28).
4. Simplify: x = 280.

So, the solution to the equation 30 - x/10 = 2 is x = 280.

Answer 3