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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, -1.2, – 3.2, -5.2, -7.2 …

(ii) Given, -10, – 6, – 2, 2 …

Solution(i):

Given here,

{{a}_{2}}-a=(-3.2)-(1.2)=-{{2}_{{}}}

{{a}_{3}}={{a}_{2}}=(-5.2)-(-3.2)=-2

{{a}_{4}}-{{a}_{3}}=(-7.2)-(-5.2)=-2

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

Therefore, d = -2 and so the given series are in A.P.

The following three terms are;

{{a}_{5}}=-7.2-2=-9.2

{{a}_{6}}=-9.2-2=-11.2

{{a}_{7}}=-11.2-2=-13.2

Solution(ii):

The terminologies and their differences are defined here.;

{{a}_{2}}-{{a}_{1}}=(-6)-(-10)=4

{{a}_{3}}-{{a}_{2}}=(-2)-(-6)=4

{{a}_{4}}-{{a}_{3}}=(2-(-2)=4

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

Therefore, d = 4 and so the given numbers are in A.P.

The following three terms are;

a5 = 2+4 = 6

a6 = 6+4 = 10

a7 = 10+4 = 14


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