There is a linear relationship between the terms. It is identified by the first term (a) and the common ratio (r). It is identified by the first term (a) and the common difference (d). In this, the ratios of every two consecutive numbers are the same. In this, the differences between every two consecutive numbers are the same. Here are the differences between arithmetic and geometric sequence: Arithmetic Sequence Thus, we have derived both formulas for the sum of the arithmetic sequence. (2)Īdding (1) and (2), all terms with 'd' get canceled.ĢS n = (a 1 + a n) + (a 1 + a n) + (a 1 + a n) + … + (a 1 + a n)īy substituting a n = a 1 + (n – 1)d into the last formula, we have Let us write the same sum from right to left (i.e., from the n th term to the first term). Then the sum of the first 'n' terms of the sequence is given by Let us take an arithmetic sequence that has its first term to be a 1 and the common difference to be d. We can use this formula to be more helpful for larger values of 'n'. Substituting these values in the sum sum of arithmetic sequence formula, We have to calculate her earnings in the first 5 years. Natalie for the first year is, a = 2,00,000. Then how much does she earn at the end of the first 5 years? Natalie earns $200,000 per annum and her salary increases by $25,000 per annum. ![]()
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