If so, find the common difference and the next three terms. How much does the load weigh after the fifth stop? CONFIDENTIALġ5 Assessment Determine whether each sequence appears to be an arithmetic sequence. CONFIDENTIALġ4 Now you try! 1) Each time a truck stops, it drops off 250 pounds of cargo. = 61,553 The odometer will read 61,553 miles 20 days later. = 60,473 + (20)54 Simplify the expression in parentheses. CONFIDENTIALġ3 Step3: Find the odometer reading for an.Īn = a1 + (n - 1) d Write the rule to find the nth term. Since you want to find the odometer reading 20 days later, you will need to find the 21st term of the sequence, so n = 21. Since the odometer reading is 60,473 miles, a1 = 60,473. Since the odometer reading will increase by 54 miles per day, d = 54. The sequence for the situation is arithmetic because the odometer reading will increase by 54 miles per day. What is the odometer reading 20 days later? Step1: Determine whether the situation appears to be arithmetic. Travel Application The odometer on a car reads 60,473. 1) 60th term: 11, 5, -1, -7, … 2) 12th term: a1 = 4.2 d = 1.4 CONFIDENTIALġ2 Step1: Determine whether the situation appears to be arithmetic. Now you try! Find the indicated term of each arithmetic sequence. CONFIDENTIALġ1 Find the indicated term of each arithmetic sequence. = 7 + (14) 3 Simplify the expression in parentheses. CONFIDENTIALġ0 Find the indicated term of each arithmetic sequence.ī) 15th term: a1 = 7 d = 3 an = a1 + (n - 1) d Write the rule to find the nth term. = 5 + (21) (-3) Simplify the expression in parentheses. an = a1 + (n - 1) d Write the rule to find the nth term. Step2: Write a rule to find the 22nd term. 5, 2, -1, -4, … The common difference is -3. A) 22nd term: 5, 2, -1, -4, … Step1: Find the common difference. CONFIDENTIALĩ Finding the nth Term of an Arithmetic Sequenceįind the indicated term of each arithmetic sequence. Finding the n th Term of an Arithmetic Sequence The nth term of an arithmetic sequence with common difference d and first term a1 is a1 = a1 + (n - 1) d. Words Numbers Algebra 1st term 2nd term 3nd term 4 th term | n th term 3 3 + (1) 2 = 5 3 + (2) 2 = 7 3 + (3) 2 = 9 3 + (n - 1) 2 a1 a1 + 1d a1 + 2d a1 + 3d a1 + (n - 1)d The pattern in the table shows that to find the n th term, add the first term to the product of (n - 1) and the common difference. CONFIDENTIALĨ Finding the n th Term of an Arithmetic Sequence You can use the first term and the common difference to write a rule for finding an. To designate any term, or the nth term, in a sequence, you write an, where n can be any number. The variable a9, read “a sub 9,” is the ninth term in a sequence. The variable a is often used to represent terms in a sequence. 1) -3, -1, 1, 3, ……… 2) 4, 1, -2, -5, … CONFIDENTIALħ The variable a is often used to represent terms in a sequence CONFIDENTIALĦ Now you try! Determine whether each sequence appears to be an arithmetic sequence. 1, 4, 9, 16, … This sequence is not an arithmetic sequence. The difference between successive terms is not the same. CONFIDENTIALĥ This sequence is not an arithmetic sequence.ī) 1, 4, 9, 16, … Step1: Find the difference between successive terms. 12, 8, 4, 0, -4, -8, -12 The sequence appears to be an arithmetic sequence with a common difference of -4. 12, 8, 4, 0, … Step2: Find the difference between successive terms. You add -4 to each term to find the next term. A) 12, 8, 4, 0, … Step1: Find the difference between successive terms. If so, find the common difference and the next three terms in the sequence. CONFIDENTIALĭetermine whether each sequence appears to be an arithmetic sequence. So the distances in the table form an arithmetic sequence with common difference 0.2. When the terms of a sequence differ by the same nonzero number d, the sequence is an arithmetic sequence and d is the common difference. Time (s) 1 2 3 4 5 6 7 8 Distance (mi) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 + 0.2 Notice that in the distance sequence, you can find the next term by adding 0.2 to the previous term. A sequence is a list of numbers that often forms a pattern. CONFIDENTIALģ Arithmetic Sequences When you list the times and distances in order, each list forms a sequence. 3) The number of times you sharpen your pencil and the length of your pencil. 2) The number of members in a family and the size of the family’s grocery bill. 1) The speed of a runner and the distance she can cover in 10 minutes. 2 Warm Up Identify the correlation you would expect to see between each pair of data sets.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |