Question

Here are the first four terms of a sequence. -1 4 9 14 Write an expression for the n th term of this sequence.​

Answer 1

• The nth term is aₙ = 5n - 6

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Given sequence:

• -1, 4, 9, 14, ...

We observe that it has a linear increase and common difference of terms is 5:

• 4 - (-1) = 9 - 4 = 14 - 9 = 5

So d = 5, a₁ = - 1, find the nth term:

• aₙ = a₁ + (n - 1)d
• aₙ = - 1 + (n - 1)*5 = - 1 + 5n - 5 = 5n - 6