Formula for the sequence is tₙ = 3n - 10.
What is an Arithmetic Progression?
- Sequence in which the difference between the two consecutive numbers is constant.
- Sequence where each term is obtained by adding the fixed number in the previous term, except the first term.
Given: Sequence
-7, -4, -1, 2, 5
Here, the first term is a = -7.
The difference between two consecutive terms is:
d = -4 - (-7) = 3
d = -1 - (-4) = 3
d = 2 - (-1) = 3
d = 5 - 2 = 3
Difference, d = 3 is constant.
Hence, the given sequence is an Arithmetic progression.
Now, in the given arithmetic sequence we have to find the formula for the general nth term of the sequence.
we have, a = -7 and d = 3, hence the formula for the nth general term will be given by:
⇒ tₙ = a + (n - 1)d
⇒ tₙ = -7 + (n - 1) × 3
⇒ tₙ = -7 + 3n - 3
⇒ tₙ = 3n - 10
Therefore, for the given sequence the explicit formula will be tₙ = 3n - 10.
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