Question

which of the following are APs? if they form an AP, find the common difference d and write three more terms? a) 1,3,9,27,------ ,b) 3, 3+√2 , 3+2√2, 3+3√2, -----
please give the answer
Step By Step ​

Answer 1

Answer:

a,b,c are said to be in AP if the common difference between any two consecutive number of the series is same ie b−a=c−b⇒2b=a+c

(i) It is not in AP, as the difference between consecutive terms is different.

(ii) It is in AP with common difference d=

2

5

−2=

2

1

,

t

n

=a+(n−1)d

a=2

t

5

=2+(5−1)

2

1

Next three terms are 4,

2

9

,5

(iii) It is in AP with common difference d=−3.2+1.2=−2 ,and a=−1.2

Next three terms are

a+(5−1)d=−9.2,

a+(6−1)d=−11.2,

a+(7−1)d=−13.2

(iv) It is in AP with common difference d=−6+10=4, and

a=−10

Next three terms are

a+(5−1)d=6,

a+(6−1)d=10,

a+(7−1)d=14

(v) It is in AP with common difference d=3+

2

−3=

2

, and

a=3

Next three terms are

a+(5−1)d=3+4

2

,

a+(6−1)d=3+5

2

,

a+(7−1)d=3+6

2

(vi) It is not in AP since 0.22−0.2



=0.222−0.22

(vii) It is in AP with common difference d=−4−0=−4 and a=0,

Next three terms are

a+(5−1)d=−16,

a+(6−1)d=−20,

a+(7−1)d=−24

(viii) It is in AP, with common difference 0, therefore next three terms will also be same as previous ones, i.e., −

2

1

(ix) It is not in AP since 3−1



=9−3

(x) It is in AP with common difference d=2a−a=a and first term is a,

Next three terms are

a+(5−1)d=5a,

a+(6−1)d=6a,

a+(7−1)d=7a

(xi) It is not in AP, as the difference is not constant.

(xii) It is in AP with common difference d=

2

and a=

2

,

Next three terms are

a+(5−1)d=5

2

=

50

,

a+(6−1)d=

72

,

a+(7−1)d=

98

(xiii) It is not in AP as difference is not constant.

(xiv) It is not in AP as difference is not constant.

(xv) It is in AP with common difference d=5

2

−1=24 and a=1,

Next three terms are

a+(5−1)d=97,

a+(6−1)d=121,

a+(7−1)d=145

hope it helps you

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Answer 2

Answer:

Step-by-step explanation:

(b) is AP

 3, 3+√2 , 3+2√2, 3+3√2 and so on

first term = a= 3

coomon difference = d =  (3+√2) - 3

                                    d  = √2

three more terms

                                3+3√2 + √2  =  3+4√2

                                 3+3√2 + √2 = 3+5√2

                                 3+3√2 + √2 = 3+6√2