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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) Given, 3, 3+√2, 3+2√2, 3+3√2
  • (ii) 0.2, 0.22, 0.222, 0.2222 ….

Solution(i):

Given here,

{{a}_{2}}-a=3=\sqrt{2}-3={{\sqrt{2}}_{{}}}

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

{{a}_{4}}-{{a}_{3}}=(3+3\sqrt{2})-(3+2\sqrt{2})={{\sqrt{2}}_{{}}}

Since, an+1 – an or the common difference remains the same every time.

Therefore, d = √2 and so the given series forms a A.P.

The following three terms are;

{{a}_{5}}=(3+\sqrt{2})+\sqrt{2}=3+4\sqrt{2}

{{a}_{6}}=(3+4\sqrt{2})+\sqrt{2}=3+5\sqrt{2}

{{a}_{7}}=(3+5\sqrt{2})+\sqrt{2}=3+6\sqrt{2}

Solution(ii):

Given here,

{{a}_{2}}-{{a}_{1}}=0.22-0.2=0.02

{{a}_{3}}-{{a}_{2}}=0.222-0.22=0.002

{{a}_{4}}-{{a}_{3}}=0.2222-0.222=0.0002

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

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

i

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