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Find the seventh term of the sequence 𝑎_𝑛 = 𝑛³ − 14.

Find the seventh term of the sequence 𝑎 sub 𝑛 is equal to 𝑛 cubed minus 14.

The seventh term of a sequence with a general term 𝑎 sub 𝑛 will be denoted 𝑎 sub seven. We can calculate this by substituting 𝑛 equals seven into our expression for the general term. 𝑎 sub seven is equal to seven cubed minus 14. We know that seven multiplied by seven or seven squared is equal to 49. This means that we can calculate seven cubed by multiplying 49 by seven. As 40 multiplied by seven is 280 and nine multiplied by seven is 63, we can find the sum of these to calculate 49 multiplied by seven, which is 343. The seventh term of the sequence is equal to 343 minus 14. This is equal to 329. We can use this method to calculate any term in a sequence when given an expression for the general term in terms of 𝑛. For example, to calculate the 20th term, we would substitute 𝑛 equals 20 into the expression.

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