SequenceDetermine an for the sequence 1,4,7,10,....

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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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