SequenceDetermine an for the sequence 1,4,7,10,....
We notice that each term is obtained by adding 3 to the preceding term. Therefore, we conclude that the given sequence is an arithmetic sequence, whose common difference is 3.
We'll note the common difference as d = 3.
an is the n-th term of the A.P. and it could be calculated using the formula of general term:
an = a1 + (n-1)*d, where a1 is the first term, n is the number of terms and d is the common difference.
a1 = 1
d = 3
an = 1 + (n-1)*3
We'll remove the brackets and we'll get:
an = 1 + 3n - 3
We'll combine like terms:
an = 3n - 2
Now, we can compute any term of the given sequence:
a2 = 3*2 - 2
a2 = 6-2
a2 = 4
a3 = 3*3 - 2
a3 = 9 - 2
a3 = 7
The formula verifies the terms from the given sequence; 1,4,7,10,...