The common difference of an arithmetic sequence is 4. The 13th term is 103. Find the general term of the arithmetic sequence.
The 5th term and the 8th term of an arithmetic sequence are 18 and 27 respctively.
a)Find the 1st term and the common difference of the arithmetic sequence.
b)Find the general term of the arithmetic sequence.
been there, done that above
To find the general term of an arithmetic sequence, you need to know the first term (a1) and the common difference (d).
We are given that the common difference (d) is 4.
The 13th term (a13) is given as 103.
We can use the formula for the nth term of an arithmetic sequence, which is given by:
an = a1 + (n−1)d
Here, a1 is the first term.
We can substitute the known values into the formula:
a13 = a1 + (13−1)4
103 = a1 + (12)4
103 = a1 + 48
To isolate a1, we subtract 48 from both sides:
55 = a1
So, the first term (a1) of the arithmetic sequence is 55.
Now, we can write the general term of the sequence using this value:
an = a1 + (n−1)d
an = 55 + (n−1)4
Simplifying, we get:
an = 55 + 4n − 4
an = 4n + 51
Therefore, the general term of the arithmetic sequence is 4n + 51.
To find the general term of an arithmetic sequence, we need to know two things: the first term and the common difference.
Given that the common difference is 4, we know that the difference between any two consecutive terms in the sequence is always 4.
We are also given that the 13th term in the sequence is 103.
Now, let's find the first term of the sequence:
To find the first term, we can use the formula:
nth term = first term + (n-1) * common difference
Substituting the known values:
13th term = first term + (13 - 1) * 4
103 = first term + 12 * 4
103 = first term + 48
To isolate the first term, we subtract 48 from both sides of the equation:
103 - 48 = first term
55 = first term
So, the first term of the arithmetic sequence is 55.
Now we can find the general term of the sequence using the formula:
nth term = first term + (n-1) * common difference
Substituting the known values:
nth term = 55 + (n-1) * 4
Therefore, the general term of the arithmetic sequence with a common difference of 4 is (55 + (n-1) * 4).