![]() Treat math as a language, while moving to rigorous proof and using logical reason for performing a particular step in a proof or derivation. Math is interesting because a few equations and diagrams can communicate volumes of information. With the right attitude and friends and teachers, doing math can be most entertaining and delightful. Maths tricky questions and answers can be transformed into fun math problems if you look at it as if it is a brainstorming session. There is nothing like hard math problems or tricky maths questions, it’s just that you haven’t explored mathematics well enough to comprehend its easiness and relatability. The golden rule is to know that maths is a mindful activity rather than a task. Compared to older times, people have a better and friendly approach to mathematics which makes it more appealing. Maths is nothing less than a game, a game that polishes your intelligence and boosts your concentration. = 2 \sum_ 0.Mathematics can be fun if you treat it the right way. Let us first decompose this sum as follows We now know that 1555 is the 311 th term, we can use the formula for the sum as follows We use the formula for the n th term as follows We need to know the rank of the term 1555. The above sequence has a first term equal to 5 and a common difference d = 5. The first few terms of a sequence of positive integers divisible by 5 is given by We now the first term and last term and the number of terms in the sequence, we now find the sum of the first 50 termsįind the sum of all positive integers, from 5 to 1555 inclusive, that are divisible by 5. We use the n th term formula to find the 50 th term The above sequence has a first term equal to 2 and a common difference d = 2. The sequence of the first 50 even positive integers is given by We have the formula that gives the sum of the first n terms of an arithmetic sequence knowing the first and last term of the sequence and the number of terms (see formula above).įind the sum of the first 50 even positive integers. The first term is 1 and the last term is 1000 and the common difference is equal to 1. The sequence of integers starting from 1 to 1000 is given by Now that we have calculated a 1 and d we use them in the n th term formula to find the 100 th formula.įind the sum of all the integers from 1 to 1000. 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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