Mathematics, 23.01.2020 14:31 gesic2003

How do i find this, what’s the formula to find the 20th term and can anyone explain the formula? will award brainliest

How do i find this, what’s the formula to find the 20th term and can anyone explain the formula? wi

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Answer from: vanessam16

f(n) = n^2 +1f(20) = 401

Step-by-step explanation:

The first differences of the sequence are ...

5-2 = 310-5 = 517-10 = 726-17 = 937-26 = 11

Second differences are ...

5 -3 = 27 -5 = 29 -7 = 211 -9 = 2

The second differences are constant, so the sequence can be described by a second-degree polynomial.

We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...

f(n) = an^2 + bn + c

Then the first three terms of the sequence are ...

f(1) = 2 = a·1^2 + b·1 + cf(2) = 5 = a·2^2 +b·2 + cf(3) = 10 = a·3^2 +b·3 +c

Subtracting the first equation from the other two gives ...

3a +b = 3

8a +2b = 8

Subtracting the first of these from half the second gives ...

(4a +b) -(3a +b) = (4) -(3)

a = 1 . . . . . simplify

Substituting into the first of the 2-term equations, we get ...

3·1 +b = 3

b = 0

And substituting the values for a and b into the equation for f(1), we have ...

1·1 + 0 + c = 2

c = 1

So, the formula for the sequence is ...

f(n) = n^2 + 1

The 20th term is f(20):

f(20) = 20^2 +1 = 401

Comment on the solution

It looks like this matches the solution of the "worked example" on your problem page.

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

Answer from: Quest

step-by-step explanation:

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