Question 2(Multiple Choice Worth 1 points)
(03.06 LC)

Determine if the sequence is algebraic or geometric, and find the common difference or ratio.

x 1 2 3 4
f(x) 5 −5 −15 −25

ANSWER OPTIONS:
Algebraic, common difference = −10
Algebraic, common difference = −1
Geometric, common ratio = −10
Geometric, common ratio = −1

The Algebraic sequence is the sequence that has a common difference between each two consecutive terms, like 2 , 5 , 8 , 11 , 14 , .......... the difference between the 5 and 2 is equal to the difference between 8 and 5, and the difference between 11 and 8 and the difference between 14 and 11
The geometric sequences is the sequence that has a common ratio between each two consecutive terms, like 3 , -9 , 27 , -81 , ...... the ratio between -9 and 3 as the ratio between 27 and -9 as the ratio between -81 and 27

→ x : 1 : 2 : 3 : 4

→ f(x) : 5 : -5 : -15 : -25

x represents the positions of the terms

f(x) represents the value of each term

∵ 1st = 5 and 2nd = -5

∵ -5 - 5 = -10

∵ 2nd = -5 and 3rd = -15

∵ -15 - (-5) = -15 + 5 = -10

∵ 3rd = -15 and 4th = -25

∵ -25 - (-15) = -25 + 15 = -10

∴ There is a common difference -10 between each two

consecutive terms

∴ The sequence is algebraic with common difference -10

The sequence is " Algebraic, common difference = −10 "

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