Question

complete series
2,2,9,9,25,25

Answer 1

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

$\huge{\gray{\mathrm{Given:-}}}$

Series :- 2,2,9,9,25,25

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$\huge{\gray{\mathrm{To \: Find:-}}}$

Next term of the series

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$\huge{\gray{\mathrm{Solution :-}}}$

When we see the series cirrectly we saw that :-

1st term and 2nd term are equal.

3rd term and 4th term are equal.

5th term and 6th term are equal.

$\rule{200}{2}$

1st Method to do it :-

Add 1st and 2nd both term and then add 5 we get 9. (2 + 2 + 5 = 9)

Add 3rd and 4th both term and then add 7 we get 25. (9 + 9 + 7 = 25)

Now,

Add 5th and 6th both term and then add 9 we get 59. (25 + 25 + 9 = 59)

So, Our next two terms will be 59.

$\LARGE{\boxed{\blue{\sf{59}}}}$

$\rule{200}{2}$

2nd method to do it.

Add 7 to the 2nd term we get 9 (2 + 7 = 9)

Add 14 to the 4th term we get 23 (9 + 14)

Add 21 to the 6th term we get 46 (25 + 21 = 46)

$\LARGE{\boxed{\blue{\sf{46}}}}$

$\rule{200}{2}$

Hence, next term can be 46 or 59