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Find the nth term 1 + 4 + 7 + 10 + 13 ⋯
We will use the concept of sequence and series in order to find the nth term.
Answer: nth-term an = 3n - 2
Let us see how we will use the concept of sequence and series in order to find the nth term.
This is an arithmetic sequence.
First-term a1 = 1
Second-term a2 = 4
Third-term a3 = 7
Fourth term a4 = 10
Difference between two terms = 3
As per arithmetic sequence formula, an = a + (n-1)d
Here, a = 1, d = 3
an = 1 + (n - 1)(3)
an = 1 + 3n - 3
an = 3n - 2
Thus, we can observe that nth-term an = 3n - 2