arithmetic sequence problem solving examples with solutions brainly

Solution. This problem can be viewed as either a linear function or as an arithmetic sequence. The table of values give us a few clues towards a formula. The problem allows us to begin the sequence at whatever n n −value we wish. It's most convenient to begin at n = 0 n = 0 and set a0 = 1500 a 0 = 1500.

An example of problem-solving steps in math is provided. Explanation: Problem-solving Steps: Problem-solving is a series of sequential steps used to respond to a well-structured problem. While there is no simple step-by-step method that works for every problem, the general procedures facilitate problem-solving and make it more meaningful.

These problems can be solved using the formulas for arithmetic sequences and series, by plugging in the given values and solving for the requested variable. The solutions to the problems are 27, 90, -64, 975, and 80 respectively. Explanation: To solve the arithmetic sequence and series problems:

Solution: Find the rule that defines the sequence using the arithmetic sequence formula. The first term is [latex]{a_1} = -9[/latex] while the common difference is [latex]d=7[/latex]. Plug these values in the formula, we get

For many of the examples above, the pattern involves adding or subtracting a number to each term to get the next term. Sequences with such patterns are called arithmetic sequences. In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference ...

The general term of an arithmetic sequence can be written in terms of its first term a1, common difference d, and index n as follows: an = a1 + (n − 1)d. An arithmetic series is the sum of the terms of an arithmetic sequence. The n th partial sum of an arithmetic sequence can be calculated using the first and last terms as follows: Sn = n(a1 ...

Definition and Basic Examples of Arithmetic Sequence. An arithmetic sequence is a list of numbers with a definite pattern.If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.. The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common ...

Arithmetic sequence problem. Converting recursive & explicit forms of arithmetic sequences. ... Review arithmetic sequences and solve various problems involving them. ... For example, one problem has f(n) = 41 - 5n, but f(1) turned out to be 36. Are we supposed to assume that f(n) always indicates that n is not equal to 1.

Solution. The general term of the sequence of even numbers is an = 2n a n = 2 n. Since n = n = the term number, we are asked to find a20 a 20. a20 = 2(20) = 40 Plug in the term-number n = 20 into the formula an = 2n a 20 = 2 ( 20) = 40 Plug in the term-number n = 20 into the formula a n = 2 n. Answer The 20th 20 th term of the sequence of even ...

Take on these Arithmetic Series Practice Problems with Answers today - get the correct answers to all ten problems and hone your skills! ... Arithmetic Series Practice Problems with Answers. Solve each problem on paper then click the ANSWER button to check if you got it right. ... The 9th term of an arithmetic sequence is [latex]57[/latex ...

Ian Pulizzotto. 6 years ago. Actually the explicit formula for an arithmetic sequence is a (n)=a+ (n-1)*D, and the recursive formula is a (n) = a (n-1) + D (instead of a (n)=a+D (n-1)). The difference is than an explicit formula gives the nth term of the sequence as a function of n alone, whereas a recursive formula gives the nth term of a ...

For example, if the first term is 2 and the common difference is 3, and we want to find the 5th term, we substitute the values into the formula: a5 = 2 + (5-1)3 = 2 + 12 = 14. So, the 5th term of this arithmetic sequence is 14.

Solution: This sequence is the same as the one that is given in Example 2. There we found that a = -3, d = -5, and n = 50. So we have to find the sum of the 50 terms of the given arithmetic series. S n = n/2 [a 1 + a n] S 50 = [50 (-3 - 248)]/2 = -6275. Answer: The sum of the given arithmetic sequence is -6275.

Sum of the First n Terms of an Arithmetic Sequence. The sum, Sn, S n, of the first n terms of an arithmetic sequence is. Sn = n 2(a1 + an) S n = n 2 ( a 1 + a n) where a1 a 1 is the first term and an a n is the n th term. We apply this formula in the next example where the first few terms of the sequence are given.

Solving Application Problems with Arithmetic Sequences. In many application problems, it often makes sense to use an initial term of a 0 a 0 instead of a 1. a 1. In these problems, we alter the explicit formula slightly to account for the difference in initial terms. We use the following formula:

Here is an explicit formula of the sequence 3, 5, 7, …. a ( n) = 3 + 2 ( n − 1) In the formula, n is any term number and a ( n) is the n th term. This formula allows us to simply plug in the number of the term we are interested in, and we will get the value of that term. In order to find the fifth term, for example, we need to plug n = 5 ...

Solution to part a) The problem tells us that there is an arithmetic sequence with two known terms which are [latex]{a_5} = - 8[/latex] and [latex]{a_{25}} = 72[/latex]. The first step is to use the information of each term and substitute its value in the arithmetic formula. We have two terms so we will do it twice.

An arithmetic sequence is a list of numbers (terms) with a constant difference (d) between each term. You add the same number to get from one term to the next. ... teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning.

Example 12.3.3. Find the fifteenth term of a sequence where the first term is 3 and the common difference is 6. Solution: To find the fifteenth term, a15, use the formula with a1 = 3and d = 6. an = a1 + (n − 1)d Substitute in the values. a15 = 3 + (15 − 1)6 Simplify. a15 = 3 + (14)6 a15 = 87.

An example of an arithmetic word problem is solving for the amount of money saved after a certain number of weeks. An example of a geometric word problem is determining the population of bacteria after a certain number of hours. Here is an example of an arithmetic word problem: Arithmetic: Jane saves $10 every week.

This online calculator can solve arithmetic sequences problems. Currently, it can help you with the two common types of problems: Find the n-th term of an arithmetic sequence given m-th term and the common difference. Example problem: An arithmetic sequence has a common difference equal to 10, and its 5-th term is equal to 52. Find its 15-th term.

Answer: The 16ᵗʰ term of this sequence is 82. Step-by-step explanation: Here, First Term = a₁ = 9. Common Difference = (d) = 2. Now, For 16ᵗʰ term, n = 16

I have attached an example of an arithmetic sequence below. This specific sequence involves decimals. Notice that to get from one term to the next, we add . 1.3 each time in order to reach the next term. In order for a sequence to be arithmetic, the difference between the terms in the sequence must remain constant at all times.