Question Video: Finding the Next Three Terms in a Sequence given Its General Formula and First Term Mathematics • 9th Grade

Find the first three terms of the sequence 𝑎_(𝑛 + 1) = 2𝑎_(𝑛) + 5, 𝑎₁ = 11 and 𝑛 ≥ 1 (𝑛 is an integer).

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Video Transcript

Find the first three terms of the sequence 𝑎 𝑛 plus one is equal to two times 𝑎 𝑛 plus five, where the first term 𝑎 one is 11, and 𝑛 is greater than or equal one, and 𝑛 is an integer.

Now, this formula tells that if we take a term and we double it, and then we add five to that, we get the value of the next term in the sequence. To calculate the second term, we double the first term and add five. And the first term is 11. That’s what we we’re told in the question. And that means the second term is two times 11 plus five, which is 22 plus five, which is 27. And now, we can use that information to work out the third term. The third term is equal to two times the second term plus five. So, that’s two times 27 plus five, which is 54 plus five, which is 59. So, now, we’ve got the first three terms, 11, 27, and 59.

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