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:
a1 =1
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,...
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