Identify the Sequence
(1/5),(3/10),(5/15),(7/20)
neither arithmetic or geometric
−40, −47, −54, −61, ... Find a29
a29 = -236
−27, −17, −7, 3, ...
Next 3 terms: 13, 23, 33
a1 = 22, d = −9
an = 22 + (n − 1) ⋅ −9
a1 = 4, r = −4
an = 4 ⋅ (−4)n-1
2 1/2 , 3, 3 1/2, 4, 4 1/2...
arithmetic
17, 11, 5, −1, ... Find a39
a39 = -211
−2, −8, −32, −128, ...
Next 3 terms: −512, −2048, −8192
a1 = 35, d = −20
an = 35 + (n − 1) ⋅ −20
a1 = 1, r = 3
an = 3n-1
-2, -4, -8, -16...
geometric
5, −5, −15, −25, ... Find a20
a20 = -185
2, 10, 50, 250, ...
Next 3 terms: 1250, 6250, 31250
a1 = −34, d = −2
an = −34 + (n − 1) ⋅ −2
a1 = −2, r = 4
an = −2 ⋅ 4n-1
-5, -10, -15, -20
arithmetic
−8, 22, 52, 82, ... Find a20
a20 = 562
3, −6, 12, −24, ...
Next 3 terms: 48, −96, 192
a1 = −22, d = −30
an = −22 + (n − 1) ⋅ −30
a1 = −3, r = −5
an = −3 ⋅ (−5)n-1
10, 30, 90, 270, 810, 2430, ...
geometric
−32, −132, −232, −332, ... Find a40
a40 = -3932
30,22,14,6…
-2,-10,-18
a1 = −38, d = −100
an = 62 − 100n
a1 = −4, r = 6
an = an-1 ⋅ 6