Question

Find the algebraic form of the sequecne

4,7,10,………..,check this sequence contains any
perfect squares or not

Answer 1

Answer:

4+3=7

7+3=10

10+3=13

13+3=16

and 16 is the square of 4.

Answer 2

Answer:

x = 4 since it is the first number in this pattern.

The next number is 7 which is 3 more than 4.

So, 7 = x + 3

10 is the following number which is 3 more than 7.

So, 10 = 7 + 3

But, 7 = x + 3

So, 10 = x + 3 + 3 = x + 6

Therefore the pattern is x, (x+3), (x+3) + 3, [(x + 3) + 3] + 3 and so on.

Here, x = 4

And as we know, $\sqrt{4} = 2$.

Therefore, the next perfect square would be (x + 3 + 3 + 3 + 3) = 4 + 12 = 16

The next perfect square is (x + 3 + 3 + 3 + 3) + 3 + 3 + 3 = 25

And the next one is [(x + 3 + 3 + 3 + 3) + 3 + 3 + 3] + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 49

So, we can see that there are many perfect squares in this sequence.

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