Can someone explain how this question is done? - Thanks

2 Answers | Add Yours

ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

In this question, you are given the kth term of a sequence. This means that if you plug in a value of k, you will get the term of the sequence numbered k. For example,

the first term, `P_1`  will have k = 1 and `P_1 = 2^(1-1)/(1!) = 1/1 = 1` ,

the second term, `P_2` , will have k = 2 and `P_2 = 2^(2-1)/(2!) = 2^1/(1*2) = 1` ,

the third term, `P_3` , will have k = 3 and `P_3 = 2^(3-1)/(3!) = 2^2/(1*2*3) = 4/6=2/3` ,

and so on.

Note that the exclamation sign after k is called "factorial" and it means multiplying all integers starting with 1 and up to k:

`k! = 1*2*3*....(k-1)*k`

So, to find `P_(k+1)` , we need to plug in k+1 instead of k, that is, substitute k+1 for every k in the expression for `P_k` and then simplify:

`P_(k+1) = 2^(k+1 - 1)/((k+1)!) = 2^k/((k+1)!)`

This corresponds to the answer choice B.

momenna's profile pic

momenna | Elementary School Teacher | (Level 1) Honors

Posted on

Picture wasn't showing up correctly, this is the question here.

This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

We’ve answered 319,622 questions. We can answer yours, too.

Ask a question