please help me!!!

Question

sandra wrote the sequence 3,6,11,18,27,...

what explicit expression can be used to find the nth term of this sequence?

Answer 1

The given expression is 3,6,11,18,27,...

To write an explicit expression for a sequence, we must identify two parts: 1.) The initial term of the sequence, and 2.) The pattern by which the sequence changes.

The initial term is 3, and if we observe the pattern, each value in the pattern is 2 more than the list of perfect squares (1, 4, 9, 16, 25, ...). If we consider the first term, A1 = 3, then the second term A2 is found by adding 2 to 2^2, the third term A3 is found by adding 2 to 3^2, and so on.

Therefore, the explicit pattern can be written as A_N = N² + 2

Answer 2

Hello, Christina,

Look for the change that occurs between each number. I set up a table and used X to represent the sequence, from 1 to whatever. Enter the data and look at what happens in the difference between each set of numbers (under Diff.) I saw a pattern: X increases by an additional 2 two each time, after I doubled the sequence number.

So I tried:

Y = 2X + 2

It seems to work.

Bob