The following question is of NCERT Book class 10th Chapter no.5, Q. 5(v). In this question you have to find that is the question an A.P or not. If it is an A.P then find the common difference and write 3 more values of the series.

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# 3, 3 + √2, 3 + 2√2, 3 + 3√2. If this question forms an A.P then find c.d and the next four terms of the series.

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Solution:3, 3+√2, 3+2√2, 3+3√2

The difference between the above valuse are:-

a_{2}–a_{1}= 3+√2-3 = √2a_{3}–a_{2}= (3+2√2)-(3+√2) = √2a_{4}–a_{3}= (3+3√2) – (3+2√2) = √2In the series the common difference is same every time.

So,

d= √2 and this series forms a A.P.Now the next three terms in the series will be:-

a_{5}= (3+√2) +√2 = 3+4√2a_{6}= (3+4√2)+√2 = 3+5√2a_{7}= (3+5√2)+√2 = 3+6√23, 3+√2, 3+2√2, 3+3√2

a_{2}–a_{1}= 3+√2-3 = √2a_{3}–a_{2}= (3+2√2)-(3+√2) = √2a_{4}–a_{3}= (3+3√2) – (3+2√2) = √2In the series the common difference is same every time.

So,

d= √2 and this series forms a A.P.Now the next three terms of the series will be:-

a_{5}= (3+√2) +√2 = 3+4√2a_{6}= (3+4√2)+√2 = 3+5√2a_{7}= (3+5√2)+√2 = 3+6√2