Question

Write an expression for the apparent nth term (a(n)) of the sequence. (Assume that n begins with 1.)

3, 4, 8, 26, 122, ...

a(n)= ?

Answer 1

34

Explanation:

Answer 2

The expression for the nth term of the given sequence is
`a(n) = a(n-1) + 2^{(n-1)`, where a(1) = 3.

The given sequence is 3, 4, 8, 26, 122, ...

To find the expression for the nth term of the sequence, we can examine the pattern and the differences between each term.

Notice that the differences between terms increase by a factor of 2 each time.

Let's consider the differences between consecutive terms:

4 - 3 = 1

8 - 4 = 4

26 - 8 = 18

122 - 26 = 96

We can see that the differences are increasing by multiplying the previous difference by 2 each time.

So, the expression for the nth term is:

a(n) = a(n-1) +
`2^{(n-1)`, where a(1) = 3.