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.