The first term of an arithmetic sequence is 2.The 12th term in the progression is 9 times bigger than the 2nd term. Find the common difference d.
2+11d = 9(2+d)
Now just find d.
Are there answers? If not then at least review the lesson, its easier that way
To find the common difference (d) of an arithmetic sequence, we can use the formula:
n-th term = a + (n - 1)d
Where:
- n is the position of the term in the sequence
- a is the first term of the sequence
- d is the common difference between terms
Let's apply this to the problem:
Given:
- The first term (a) is 2
- The 12th term is 9 times bigger than the 2nd term
We need to determine the common difference (d).
Let's first find the 2nd term in the sequence. Using the formula, plug in the values:
2nd term = a + (2 - 1)d
Since the first term (a) is 2, we have:
2nd term = 2 + (2 - 1)d
Simplify:
2nd term = 2 + d
Now, let's find the 12th term in the sequence using the same formula:
12th term = a + (12 - 1)d
Given that the 12th term is 9 times bigger than the 2nd term, we have:
12th term = 9 * (2nd term)
Substituting the value of the 2nd term, we get:
12th term = 9 * (2 + d)
Simplify:
12th term = 18 + 9d
Now we can set up an equation using the information we derived:
18 + 9d = 12th term
Since the 12th term is 9 times bigger than the 2nd term, we have:
18 + 9d = 9 * (2 + d)
Simplify:
18 + 9d = 18 + 9d
As we can see, the equation is true for any value of d. This means that the common difference (d) could potentially be any real number, as long as it satisfies the arithmetic sequence condition.