Question

Find the common difference if AP is √2,√8, √18, √32 …​

Answer 1

Step-by-step explanation:

here is your answer mate..

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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Answer 2

Answer:

√2

Step-by-step explanation:

√2,√8,√18

can be written as

√2, 2√2, 3√2

therefore

a1=√2

a2 =2√2

a3=3√2

a2-a1=a3-a2

2√2 - √2= 3√2 - 2√2

d=√2