Math  /  Algebra

QuestionThe nth n^{\text {th }} term of a sequence is given by 2n+52 n+5 Work out the first three terms of this sequence. a) How much does the sequence go up by between each term? b) Explain how you could have used the nth n^{\text {th }} term rule to answer part a) without working out any of the terms.

Studdy Solution
Explain how the nth n^{\text{th}} term formula can be used to find the difference:
The nth n^{\text{th}} term formula is an=2n+5 a_n = 2n + 5 . The coefficient of n n (which is 2) represents the constant difference between consecutive terms in an arithmetic sequence. Therefore, without calculating individual terms, we can determine that the sequence increases by 2 between each term.
The first three terms of the sequence are 7, 9, and 11. The sequence increases by 2 between each term. The nth n^{\text{th}} term rule directly indicates this increase.

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