>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Determine whether each sequence is an arithmetic sequence. 1. 0, 2, 5, 9, 14, . .. 2. 37, 34, 31, 28, … 3. − 1 3 , − 17 6 , − 16 3 , … Given the following formulas, find the first four terms of the sequence (An example is provided.) 1 = 0 4. 1 = −4 5. = −5 + 2 = −1 + 6 = −1 + 2 2 = 1 + 6 = 0 + 6 = 3 = 2 + 6 = 6 + 6 = 4 = 3 + 6 = 12 + 6 = ∴ ℎ , , ,
Write an explicit and recursive formula for the following arithmetic sequences: −4, −6, −8, −10, … 6. 84,71,58,45, … 7. -3, -1, 1, … Explicit: = 1 + ( − 1)() Explicit: Explicit: = −4 + ( − 1)(−2) = −4 − 2 + 2 = − − Recursive: = − − Recursive: Recursive: Find the next three terms of each arithmetic sequence. 8. 10, 13, 16, 19, … 9. −14, −19, −24, … 10. 3 5 , 7 10 , 4 5 , … _____, _____, _____ _____, _____, _____ _____, _____,_____ Use the explicit formula to help solve each problem. an = a1 + (n-1)d 11. 3, 7, 11, 15, … 12. −5, −7, −9, … 13. 2 9 , 5 9 , 8 9 , … _______ _________ _________ 38th term 71st term 24th term ⋆14. An arithmetic sequence has a common difference of −4 and its 37th term is 10. Find the first term. ⋆15. How many total terms are there in the following sequence? 7, 10, 13, … , 391, 394
More on Arithmetic Sequences: 1) In the following arithmetic sequences, find the missing term/ a. 2, ____, 26, … b. ____, 13, ____, 3 ,… c. 5, _____, _____, 9.5, … 2) Which term of the arithmetic sequence 3, 8, 13, 18, … is 78? 3) Find the number of terms in each of the following arithmetic sequences: a. 7, 13, 19, …, 205 b. 18, 15.5, 13, … , -47 4) Check whether -150 is a term in the arithmetic sequence 11, 8, 5, 2, … . 5) Find the 31st term of an arithmetic sequence whose 11th term is 38 and 16th term is 73. 6) The 17th term of an arithmetic sequence exceeds its 10th term by 7. Find the common difference. 7) Which term of the arithmetic sequence 3, 15, 27, 39 ,… will be 132 more than its 54th term?