Now use the value of d in one of the equations to find a 1. Subtract the right and left term of the two equations to obtain We obtain a system of 2 linear equations where the unknown are a 1 and d. We use the n th term formula for the 5 th and 15 th terms to write Now that we know the first term and the common difference, we use the n th term formula to find the 15 th term as follows.Īn arithmetic sequence has a its 5 th term equal to 22 and its 15 th term equal to 62. The above equation allows us to calculate a 1. We use the n th term formula for the 6 th term, which is known, to write Use the value of the common difference d = -10 and the first term a 1 = 200 in the formula for the n th term given above and then apply it to the 20 th termĪn arithmetic sequence has a common difference equal to 10 and its 6 th term is equal to 52. The first term of an arithmetic sequence is equal to 200 and the common difference is equal to -10. The 50 th term is found by setting n = 50 in the above formula. Use the value of the common difference d = 3 and the first term a 1 = 6 in the formula for the n th term given above Find a formula for the n th term and the value of the 50 th term The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. An online calculator to calculate the sum of the terms in an arithmetic sequence. The sum s n of the first n terms of an arithmetic sequence is defined byĪrithmetic Series Online Calculator. The formula for the n th term a n of an arithmetic sequence with a common difference d and a first term a 1 is given by Arithmetic Sequences Problems with SolutionsĪrithmetic sequences are used throughout mathematics and applied to engineering, sciences, computer sciences, biology and finance problems.Ī set of problems and exercises involving arithmetic sequences, along with detailed solutions are presented.
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