Vince604 said:Homework Statement
In an arithmetic sequence, the 11th term is 53 and the sum ofof the 5th and 7th terms is 56. Find the first 3 terms of the sequence.
Homework Equations
The Attempt at a Solution
I'm trying to use the formula: tn= t1+(n-1)d but don't have right numbers. please show me step by step would be really helpful. Thanks
Vince604 said:Homework Statement
In an arithmetic sequence, the 11th term is 53 and the sum ofof the 5th and 7th terms is 56. Find the first 3 terms of the sequence.
Homework Equations
The Attempt at a Solution
I'm trying to use the formula: tn= t1+(n-1)d but don't have right numbers. please show me step by step would be really helpful. Thanks
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
An arithmetic sequence is a series of numbers in which each term is obtained by adding a constant value, called the common difference, to the previous term. For example, if the first term is 2 and the common difference is 3, the sequence would be 2, 5, 8, 11, and so on.
To find the first three terms of an arithmetic sequence using the formula tn= t1+(n-1)d, you first need to know the value of t1 (the first term) and d (the common difference). Then, you can simply plug in the value of n for each term you want to find. For example, if t1 is 2 and d is 3, the first three terms would be t1=2, t2= 2+3=5, and t3= 2+2(3)=8.
If you don't know the common difference, you can still find the first three terms of an arithmetic sequence by using the given information about the sequence. For example, if you know that the first term is 2 and the fifth term is 14, you can set up a system of equations to solve for both t1 and d. Once you have those values, you can use the formula tn= t1+(n-1)d to find the first three terms.
Yes, this formula can be used to find any term in an arithmetic sequence. You just need to know the value of t1, d, and the term number (n) that you want to find. For example, if you wanted to find the 10th term in a sequence with t1= 2 and d= 3, you would plug in n= 10 and solve for tn.
Yes, there are other methods for finding the first three terms of an arithmetic sequence. One method is to create a table or list of the terms in the sequence and use patterns or relationships between the terms to find the first three. Another method is to graph the sequence and find the first three terms by identifying the points on the graph. However, using the formula tn= t1+(n-1)d is the most efficient and reliable method for finding the first three terms of an arithmetic sequence.