Question

What is the next three terms of the following sequences √2, √12 + √2, 24 +√2, .36 + √2, 48 + √2?​

Answer 1

Its simple

its in form 12n +√12 form

vvhere n= 0, 1 , 2 ,3 ,4 ..............

so next three terms are

• 60 +√12
• 72+√12
• 84+√12

Answer 2

SOLUTION

TO DETERMINE

The next three terms of the sequence

√2 , 12 + √2 , 24 + √2 , 36 + √2 , 48 + √2

EVALUATION

Here the given sequence is

√2 , 12 + √2 , 24 + √2 , 36 + √2 , 48 + √2

1st term = √2

2nd Term = 12 + √2

3rd term = 24 + √2

4th term = 36 + √2

5th term = 48 + √2

∴ 3rd term - 2nd term = 2nd term - 1st term

So the sequence is an arithmetic sequence

Common Difference = 12 + √2 - √2 = 12

Thus we get -

6th term = 48 + √2 + 12 = 60 + √2

7th term = 60 + √2 + 12 = 72 + √2

8th term = 72 + √2 + 12 = 84 + √2

FINAL ANSWER

Hence the required next three terms are

60 + √2 , 72 + √2 , 84 + √2

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