Q. 4 L4.5( 15 Votes )

Which of the following are APs? If they form an AP, find the common difference d and write three more terms.

√2, √8, √18, √32

Answer :

He above series can be re written as

√2, √8, √18, √32


√2, √(22 × 2), √(32 × 2), √(42 × 2)


√2, 2√2, 3√2, 4√2,…..


For a series to be in AP, the common difference (d) should be


Equal.


d1 = second term – first term = 2√2 – √2 = √2


d2 = Third term - Second term = 3√2 – 2√2 =


Since common difference is same the above series is in AP.


The next three terms will be the 5th, 6th, 7th.


5th term will be given by


a + (5-1)d = a + 4d = √2+ 4(√2) = 5√2 = √50


6th term is a + (6-1)d = a + 5d = √2 + 5(√2) = 6√2 = √72


7th term is a + (7-1)d = a + 6d = √2 + 6(√2) = 7√2 = √98.


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