Question

The next number in the sequence 4/23, 9/24, 16/24, 25/26, 36/27 is

Answer 1

SOLUTION

TO DETERMINE

The next number in the sequence

$\displaystyle \sf{ \frac{4}{23} \: , \: \frac{9}{24} \: ,\: \frac{16}{25} \: ,\: \frac{25}{26} \: , \: \frac{36}{27} }$

EVALUATION

Here the given sequence is

$\displaystyle \sf{ \frac{4}{23} \: , \: \frac{9}{24} \: ,\: \frac{16}{25} \: ,\: \frac{25}{26} \: , \: \frac{36}{27} }$

So the General Term of the sequence is

$\displaystyle \sf{ \frac{ {(n + 1)}^{2} }{22 + n} \: } \: \: \: Where \: \: n \in \mathbb{N}$

Hence the required next term

= 6 th term

$\displaystyle \sf{ = \frac{ {(6 + 1)}^{2} }{22 + 6} \: }$

$\displaystyle \sf{ = \frac{ {7}^{2} }{28} \: }$

$\displaystyle \sf{ = \frac{49}{28} \: }$

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