Subscript help

[Fdelpesce]

How do you solve a problem that includes a subscript? I know they are different than an exponent but I am clueless of how to solve them. In order to help understand the problem the information that has ** around it is a subscript because I'm not sure how to type a subscript.. The problem I am trying to solve is:

In a certain sequence the term X*n* is given by the formula X*n* = 2x*n-1* - 1/2(x*n-2*) for all n > or equal to 2. If x*0* = 3 and x*1* = 2, what is the value of x*3*? Any help is greatly appreciated and please explain how you did your calculations with the subscripts!

Thank you

[dabral]

The subscripts problems typically show up in sequence problems. The subscript notation is often used to depict the terms of a sequence. For example, the first term of a sequence is often written as x_1(I am using _ instead of a subscript), the second term is x_2, and so on. The nth term is then written as x_n.

When you see a relationship such as x_n = x_(n-1) + 5, then in words it means that the nth term is five more than the (n-1)th term, or in other words the current term is five more than the prior term. If in this particular case, we are told that the first term, x_1 is 2, then we can use the above rule to compute the subsequent terms. We would say, x_2 = x_1 + 5(here we replace n as 2), and we find that x_2 is 7. In this simple case, one could directly add 5 to 2 and compute the next term, but I wanted to illustrate how to apply this type of rule.

As for the problem that you asked in the original post, you can watch the video explanation at this link:
https://www.gmatquantum.com/og13/160-pro ... ition.html

Cheers,
dabral

[gmattest001]

How do you solve a problem that includes a subscript? I know they are different than an exponent but I am clueless of how to solve them. In order to help understand the problem the information that has ** around it is a subscript because I'm not sure how to type a subscript.. The problem I am trying to solve is:

In a certain sequence the term X*n* is given by the formula X*n* = 2x*n-1* - 1/2(x*n-2*) for all n > or equal to 2. If x*0* = 3 and x*1* = 2, what is the value of x*3*? Any help is greatly appreciated and please explain how you did your calculations with the subscripts!

Thank you

its related to the sequence :-
we know x*0* =3 and x*1* = 2
let solve for x*3* = 2x*(3-1)*-1/2(x*(3-2)*) -- as per definition X*n* = 2x*n-1* - 1/2(x*n-2*) for all n > or equal to 2.
=2x*2*-1/2(x*1*)
=2x*2*-1/2(2) -- give that x*1*=2
=2x*2* -1 ----------------Equation 1
Here we do not know x*2* -- lets solve it first and let keep this here only say it Equation 1

x*2*=2x*(2-1)*-1/2(x*(2-2)*)
=2x*1*-1/2(x*0*)
=2(2) -1/2(3) -- give that x*1*=2 and x*0*=3
=4-3/2

put this value in the Equation 1
=2(4-3/2)-1
hence this is the answer..

I hope this is easy to understand ...Click on thanks icon if found helpful.

[Jim@StratusPrep]

The subscript is just a reference to the term number. The variable with subscript is a place holder for that term number's value.