Question

Sequences and Functions

Tell whether the sequence is arithmetic. If it is, identify the common difference. ( 1/2, 1/3, 1/6, 0 … )




Tell whether the sequence is arithmetic. If it is, identify the common difference. (-3, -7, -10, -14 …)

Answer 1

-7

Explanation:

did the deltamth

Answer 2

(a)Common Difference
`=-(1)/(6)`

(b)Not an arithmetic sequence.

Explanation:

An arithmetic sequence is a sequence in which the next term is obtained from the previous term by the addition of a common constant.

(a)Given the sequence:

`(1)/(2), (1)/(3),(1)/(6),0,\cdots\\(1)/(3)-(1)/(2)=-(1)/(6)\\(1)/(6)-(1)/(3)=-(1)/(6)\\0-(1)/(6)=-(1)/(6)`

Clearly, this is an arithmetic sequence and the common difference is
`-(1)/(6)`

(b)Given the Sequence:

-3, -7, -10, -14 …

-7-(-3)=-7+3=-4

-10-(-7)=-10+7=-3

-14-(-10)=-14+10=-4

This is not an arithmetic sequence as the constant term is not the same all true.