Which sequences are geometric sequences? Check all that apply.
4, 2, 1, One-half,One-fourth,...
−2, 3, −4, 5, −6, …
2, 6, 18, 54, 162, …
−4, −16, −64, −256, …
−2, −4, −12, −48, −240, …
Answers
Step-by-step explanation:
HEYA ^^^^
GEOMETRICAL SEQUENCES ARE THE SEQUENCES THAT HAVE COMMON RATIO BETWEEN NUMBERS....
4, 2 , 1 , 1/2, 1/4
THIS IS A SEQUENCE AS THEIR RATIOS ARE EQUAL
4/2= 2/1 = 1/0.5= 0.5/0.25
-2,3,-4,5,-6 IS NOT A G.P.
2,6,18,54,162 IS A GP AS RATIO IS 3 FOR ALL.
-4,-16,-64,-256 IS A GP AS RATIO IS 4 FOR ALL.
-2,-4,-12,-48,-240 IS NOT A GP...
##VIRATANMOL.......
FOLLOW ME♤♤♤
Given : Few Sequnces are given 4, 2, 1, One-half,One-fourth,... , −2, 3, −4, 5, −6, … , 2, 6, 18, 54, 162, … , −4, −16, −64, −256, … , −2, −4, −12, −48, −240, …
To find : Which sequences are geometric sequences?
Solution:
sequences are geometric sequences
if Tₙ₊₁ / Tₙ = Constant = Common Ration
4, 2, 1, One-half,One-fourth,...
2/4 = 1/2 = (1/2)/1 = (1/4)/(1/2)
1/2 = 1/2 = 1/2 = 1/2
Hence 4, 2, 1, One-half,One-fourth,... is geometric sequence
−2, 3, −4, 5, −6, …
3/-2 ≠ -4/3 ≠ 5/-4 ≠ - 6/5
Hence not a geometric sequence
2, 6, 18, 54, 162, …
6/2 =18/6 = 54/18 = 162/54
3 = 3 = 3 = 3
Hence 2, 6, 18, 54, 162, … is geometric sequence
−4, −16, −64, −256, …
= -16/-4 = -64/-16 = -256/-64
4 = 4 = 4
Hence −4, −16, −64, −256, … is geometric sequence
−2, −4, −12, −48, −240, …
-4/-2 ≠ -12/-4 = -48/-12 ≠ -240/-48
2 ≠ 3 ≠ 4 ≠ 5
Hence not a geometric sequence
below are geometric sequence
4, 2, 1, One-half,One-fourth,...
2, 6, 18, 54, 162, …
−4, −16, −64, −256, …
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