Question

Prove that the sum of any number of terms of the arithmetic sequence 16,24,32.... Starting from the first, added to 9gives a perfect square

Answer 1

Step-by-step explanation:

$S_{n} = \frac{n}{2} (a+l)$             (a = first term, l=last term)

Sum of 1st term + 9 = 16 + 9 = 25

Sum of 2nd term +9

       $S_{2} = \frac{2}{2}(16+24)$ +9

                               =40 + 9  = 49

25, 49 are perfect squares.

So, we can prove that the sum of any number of terms of the arithmetic sequence 16,24,32.... Starting from the first, added to 9gives a perfect square.

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