!_,_,_,9,730,_,... terms in the sequence above are created such that each term after the first term is 1 more than the cube of the perceding term. what is the value of the first term in the sequence??
To find the value of the first term in the sequence, let's analyze the pattern given. Each term after the first term is 1 more than the cube of the preceding term.
We are given the terms _, _, _, 9, 730, _, ...
Let's calculate the cubes of the preceding terms:
1^3 = 1
2^3 = 8
3^3 = 27
From the given pattern, we can see that the first term must be 1 less than 9, which is 8.
Therefore, the value of the first term in the sequence is 8.
To find the value of the first term in the sequence, we need to understand the pattern used to generate the sequence.
Let's break down the given information:
- Each term after the first term is 1 more than the cube of the preceding term.
- We have some missing values indicated by underscores (_) in the sequence.
Let's start filling in the values step by step:
The first term is unknown, so we'll represent it as 'x' or any other variable.
1st term: x
2nd term: 1 more than the cube of the preceding term. So, the 2nd term is (x^3 + 1).
3rd term: 1 more than the cube of the preceding term. The 3rd term is ((x^3 + 1)^3 + 1).
4th term: 9
5th term: 730
6th term: 1 more than the cube of the preceding term. The 6th term is ((730^3 + 1)^3 + 1).
Now, let's put the given information into equation form:
x, (x^3 + 1), ((x^3 + 1)^3 + 1), 9, 730, (((730^3 + 1)^3 + 1)^3 + 1), ...
From the given sequence, we can see that the 4th term is 9 and the 5th term is 730.
So the sequence looks like:
x, (x^3 + 1), ((x^3 + 1)^3 + 1), 9, 730, (((730^3 + 1)^3 + 1)^3 + 1), ...
To solve for x, we need to find the value of the first term.
By comparing the sequence with the given terms, we can say that the first term in the sequence is 9.
Therefore, the value of the first term in the sequence is 9.