Calculating nth Term of Sequences: What Now?

AI Thread Summary
The discussion revolves around calculating the nth term of two sequences and clarifying a homework question. The first sequence's nth term is identified as -2n + 4, while the second sequence's nth term is 2n - 24. The key question is determining the value of n for which the first sequence's term equals four times the second sequence's term. After clarification, the confusion about the question is resolved. The focus is on solving the equation a_n = 4b_n for n.
BerriesAndCream
Messages
7
Reaction score
2
Homework Statement
The nth term of the sequence 2, 0, -2, -4, -6 ... is 4 times the nth term of the sequence -22, -20, -18, -16, -14, ... Work out the value of n.
Relevant Equations
.
I don't understand what the question is asking.

the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.
 
Physics news on Phys.org
BerriesAndCream said:
Homework Statement:: The nth term of the sequence 2, 0, -2, -4, -6 ... is 4 times the nth term of the sequence -22, -20, -18, -16, -14, ... Work out the value of n.
Relevant Equations:: .

I don't understand what the question is asking.

the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.
If ##a_n = -2n + 4## is the n-th term of the first sequence, and ##b_n = 2n - 24## is the n-th term of the second sequence, what they're asking is this: For which value of n is ##a_n = 4b_n##?
 
Mark44 said:
If ##a_n = -2n + 4## is the n-th term of the first sequence, and ##b_n = 2n - 24## is the n-th term of the second sequence, what they're asking is this: For which value of n is ##a_n = 4b_n##?
oh... all clear now. thank you.
 
  • Like
Likes WWGD and berkeman
The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.

Similar threads

Back
Top