Math, asked by rushipatel120506, 7 months ago

1. Which of the following list of numbers form
an AP? If they form an AP, write the next
two terms: 3, 3+ 2, 3+ 78, 3+ 718 ....​

Answers

Answered by Anonymous
1

Answer:

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Step-by-step explanation:

(i) 4,10,16,22,…

From the question, it is given that,

First-term a=4

Then, difference d

=10−4=6

16−10=6

22−16=6

Therefore, common difference d=6

Hence, the numbers are form A.P.

(ii) −2,2,−2,2,…

From the question, it is given that,

First term a=−2

Then, difference d=−2−2=−4

−2−2=−4

2−(−2)=2+2=4

Therefore, common difference d is not the same in the given numbers.

Hence, the numbers are not form A.P.

(iii) 2,4,8,16,…

From the question, it is given that,

First term a=2

Then, difference d=4−2=2

8−4=4

16−8=8

Therefore, common difference dis not the same in the given numbers.

Hence, the numbers are not form A.P.

(iv) 2,5/2,3,7/2,…

From the question, it is given that,

First term a=2

Then, difference d=5/2−2=(5−4)/2=1/2

3−5/2=(6−5)/2=1/2

7/2−3=(7−6)/2=1/2

Therefore, common difference d=1/2

Hence, the numbers are form A.P.

(v)−10,−6,−2,2,…

From the question, it is given that,

First term a=−10

Then, difference d

=−6−(−10)=−6+10=4

−2−(−6)=−2+6=4

2−(−2)=2+2=4

Therefore, the common difference d=4

Hence, the numbers are form A.P.

(vi) 1

2

,3

2

,5

2

,7

2

,…

From the question, it is given that,

First term a=1

2

=1

Then, difference d

=3

2

−1

2

=9−1=8

5

2

−3

2

=25−9=16

7

2

−5

2

=49−25=24

Therefore, the common difference d is not same in the given numbers.

Hence, the numbers are not form A.P.

(vii)1,3,9,27,…

From the question, it is given that,

First term a=1=1

Then, difference d=3−1=2

9−3=6

27−9=18

Therefore, common difference dis not same in the given numbers.

Hence, the numbers are not form A.P.

(viii)

2

,

8

,

18

,

32

,…

Given numbers can be written as,

2

,2

2

,3

2

,4

2

,…

From the question, it is given that,

First-term a=V2

Then, difference d=2

2

2

=

2

3

2

−2

2

=

2

4

2

−3

2

=

2

Therefore, common difference d=

2

Hence, the numbers are form A.P.

(ix ) a,2a,3a,4a,…

From the question, it is given that,

First term a=a

Then, difference d=2a−a=a

3a−2a=a

4a−3a=a

Therefore, common difference d=a

Hence, the numbers are form A.P.

(x) a,2a+1,3a+2,4a+3,…

From the question it is given that,

First term a=a

Then, difference d=(2a+1)−a=2a+1−a=a+1

(3a+2)−(2a+1)=3a+2−2a−1=a+1

(4a+3)−(3a+2)=4a+3−3a−2=a+1

Therefore, common difference d=a+1

Hence, the numbers are form A.P.

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