How to get the formula of general term of a sequence? Explain this if the sequence is 7,10,13,...

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.