How to get the formula of general term of a sequence? Explain this if the sequence is 7,10,13,...
Analyzing the terms of the given sequence, we conclude 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.
The formula for the general term of an arithmetic progression is:
an = a1 + (n-1)*d, where a1 is the first term, n is the number of terms and d is the common difference.
a1 = 7
d = 3
an = 7 + (n-1)*3
We'll remove the brackets and we'll get:
an = 7 + 3n - 3
We'll combine like terms:
an = 3n + 4
Finding out the expression of the general term of the sequence, we can generate any term we wish:
Therefore, the formula that gives the general term of the arithmetic progression is: an = 3n + 4.