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Home » Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
Arithmetic Progression | CBSE | Class 10 | Maths | NCERT
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(i) √3, √6, √9, √12 …

(ii) 12, 32, 52, 72 …

Solution(i):

Given here,

{{a}_{2}}-{{a}_{1}}=\sqrt{6}-\sqrt{3}=\sqrt{3}*\sqrt{2}-\sqrt{3}=\sqrt{3}(\sqrt{2}-1)

{{a}_{3}}-{{a}_{2}}=\sqrt{9}-\sqrt{6}=3-\sqrt{6}=\sqrt{3}(\sqrt{3}-\sqrt{2})

{{a}_{4}}-{{a}_{3}}=\sqrt{12}-\sqrt{9}=2\sqrt{3}-\sqrt{3}*\sqrt{3}=\sqrt{3}(2-\sqrt{3})

Since, an+1 – an or the common difference varies from time to time.

Therefore, the given series does not form a A.P.

Solution(ii):

Given here,

{{a}_{2}}-{{a}_{1}}=9-1=8

{{a}_{3}}-{{a}_{2}}=25-9=16

{{a}_{4}}-{{a}_{3}}=49-25=24

Since, an+1 – an or the common difference varies  from time to time.

Therefore, the given series does not form a A.P.

i

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