University:
Davenport University
Course:
MATH 120 | College Mathematics
Academic year:

2022
Views:

49

Pages:

2
Author:

Adrian Davila

Date: ___________________ Arithmetic and Geometric Sequences Worksheet Arithmetic Sequence - is a sequence of terms that have a common _________________ between them. Geometric Sequence - is a sequence of terms that have a common _________________ between them. General Term: General Term: an = 1. 2. an = Are the following sequences arithmetic, geometric, or neither? If they are arithmetic, state the value of d. If they are geometric, state r. a) 6, 12, 18, 24, ... _____________________________________________________ b) 6, 11, 17, ... _____________________________________________________ c) 2, 14, 98, 686, ... _____________________________________________________ d) 160, 80, 40, 20, ... _____________________________________________________ e) -40, -25, -10, 5, .... _____________________________________________________ f) 7, -21, 63, -189, ... _____________________________________________________ For the following arithmetic sequences, find a and d and state the formula for the general term. Don’t forget to simplify! a) - 10, - 4, 2, 8, 14, ... b) 10, 8, 6, 4, ... c) 36, 31, 25, 21, ... 3. Use your formula from question 2c to find the values of a7 and a20 . 4. For the following geometric sequences, find a and r and state the formula for the general term. a) 1, 3, 9, 27, ... b) 12, 6, 3, 1.5, ... c) 9, -3, 1, ... 5. Use your formula from question 4c) to find the values of the a4 and a12 6. Find the number of terms in the following arithmetic sequences. Hint: you will need to find the formula for tn first! a) 2, 5, 8, ..... , 299 b) 9, 5, 1, ..... - 251. Answers: 1a) arithmetic d = 6 b) neither c) geometric r = 7 d) geometric r = 0.5 or r = ½ e) arithmetic d = 15 f) geometric r = -3 2a) a = -10; d=6; tn =6n-16 b) a = 10; d=-2; tn =-2n+12 c) a = 36; d=-5; tn = - 5n+41 3. t7 =6; t2 0 = -59 4. a) a = 1; r = 3; tn = 1(3)n –1 b) a = 12; r = ;a c) a = 9; r = - 3; tn = 9(-3)n –1 5. t4 = -243 t1 2 = -177147 6. a) tn = 3n-1; n = 100 b) tn = -4n+13; n=66