In an arithmetic sequence, the first term is 5, and the fifth term is 21. What is the second term? Help please ASAP!!
If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:
an = a1 + ( n - 1 ) * d
In this case:
a1 = 5
n = 5
a5 = 21
an = a1 + ( n - 1 ) * d
a5 = a1 + ( 5 - 1 ) * d
21 = 5 + 4 * d
21 - 5 = 4 d
16 = 4 d Divide both sides with 4
16 / 4 = 4 d / 4
4 = d
d = 4
a2 = a1 + d
a2 = 5 + 4
a2 = 9
The increase per term is (21 - 5)/(5 - 1)
= 16/4 = 4
Add 4 to the first term to get the second term
1890
Why did the arithmetic sequence go to therapy? Because it couldn't find a common difference!
But don't worry, I'll help you out. In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. So, let's find the common difference between the terms.
To get from the first term (5) to the fifth term (21), we need to add the common difference 4 times. So, the common difference can be calculated by (21 - 5) / 4 = 4.
Since the first term is 5 and the common difference is 4, we can find the second term by adding 4 to the first term: 5 + 4 = 9.
So, the second term in the arithmetic sequence is 9. Keep smiling!
To find the second term of an arithmetic sequence, you need to find the common difference between terms and then apply it to the given information.
In an arithmetic sequence, each term is obtained by adding a constant value called the common difference (d) to the previous term.
Let's find the common difference first.
To find the common difference, subtract the first term from the fifth term:
Common difference (d) = fifth term - first term
= 21 - 5
= 16
We have found that the common difference (d) is 16.
Now we can find the second term by adding the common difference to the first term:
Second term = first term + common difference
= 5 + 16
= 21
Therefore, the second term of the arithmetic sequence is 21.