If the expression f^2+g^4-2f+1 is rewritten in the form a^2+(g^2)^2, what must be the value of a?

√(f^2 - 2f + 1) = a

Step-by-step explanation:

We have that:

f^2+g^4-2f+1 =  a^2+(g^2)^2

And we want to find the value of a, so we should isolate it.

f^2 + g^4  - 2f + 1 = a^2 + g^(2*2) = a^2 + g^4

where i used that (x^y)^z = x^(y*z)

We can remove the term g^4 in both sides of the equation and get:

f^2 - 2f + 1 = a^2

now we can apply the square rooth to both sides and get

√(f^2 - 2f + 1) = a

So we just found the value of a.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

step-by-step explanation: