Video: Finding the Terms of a Sequence given Its General Term

Find the first five terms of the sequence whose general term is given by 𝑎_(𝑛) = 𝑛(𝑛 − 34), where 𝑛 ≥ 1.

02:31

Video Transcript

Find the first five terms of the sequence whose general term is given by 𝑎 sub 𝑛 is equal to 𝑛 multiplied by 𝑛 minus 34, where 𝑛 is greater than or equal to one.

In order to find the first five terms of a sequence where 𝑛 is greater than or equal to one, we need to substitute the numbers one, two, three, four, and five into the general formula. This will give us values for 𝑎 sub one through 𝑎 sub five.

When 𝑛 is equal to one, we have one multiplied by one minus 34. Using our order of operations, we need to work out the calculation inside the parentheses or brackets first. One minus 34 is equal to negative 33. Multiplying this by one gives us negative 33. This is the first term of the sequence. When 𝑛 equals two, we have two multiplied by two minus 34. This simplifies to two multiplied by negative 32.

Recalling that multiplying a positive number by a negative number gives a negative answer, the second term in the sequence is negative 64. When 𝑛 is equal to three, we have three multiplied by three minus 34. Three minus 34 is negative 31. And multiplying this by three gives us negative 93. We repeat this for 𝑛 equals four, giving us a fourth term of negative 120. When 𝑛 is equal to five, 𝑛 multiplied by 𝑛 minus 34 is negative 145.

The first five terms of the sequence where the general term is 𝑎 sub 𝑛 equals 𝑛 multiplied by 𝑛 minus 34 are negative 33, negative 64, negative 93, negative 120, and negative 145.

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