Mathematics, 28.07.2019 04:34, hectorgonzalejr333

In the equation $a_{n}$ = $a_{n}$ (r)^n-1what does the n-1 mean?

Answers: 1

Show answers

Answers

I'm pretty sure you mean $a_n = a_1 (r)^{n-1}$ where a₁ is the first term of the geometric sequence and r is the common ratio. the n is the nth term.the n-1 makes sure that the number n is exactly what it means.it basically aligns the exponent to what you want.consider this example. we have the first term a₁ be 3 and the common ratio r be 2. the formula for this geometric sequence is therefore $a_n = 3(2)^{n-1}$ the first term is 3. since the common ratio is 2, the second term should be 6. the third term should be 12. the second term, we can set n = 2 and get it. the n - 1 part will subtract 1 from n to get the correct exponent for the second term. $a_2 = 3(2)^{2-1} = 3(2)^1 = 6$ and the third term would be aligned as well for n = 3: $a_3 = 3(2)^{3-1} = 3(2)^{2} = 12$ ======now, if the formula were simply $a_n = 3(2)^n$ , you would not get the second term if you have n = 2: $a_2 = 3(2)^2 = 3(4) = 12$ 12 is supposed to be the third term. so we needed that n-1 to align ourselves to what we want, otherwise we won't be able to say intuitively that "second: n = 2", "third: n = 3", "fourth: n = 4", etc.

answered: Guest

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}

answered: Guest

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,