Question

509,68,429,140,365, ?​

Answer 1

Answer:

196

Step-by-step explanation:

509-441=68 (441=21²)

68+361=429 (361=19²)

429-289=140 (289=17²)

140+225=365 (225=15²)

365-169=196 (169=13²)

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Answer 2

Answer:

The next number is 196.

i.e.,509,68,429,140,365,196

Step-by-step explanation:

Given:

Sequence:

509,68,429,140,365,...

To find:

The next number

Solution:

Now, our aim is to find the next number in the sequence.

The relation between the numbers in the sequence is

• Firstly, consider the first number, i.e.509.

             Let us consider the number 21.

             Taking square on the number 21.

             We have,$21^{2}=441$

             Subtracting 441 from 509, we have  

             $509-441= 68$

        We get the answer as 68, which is the second number in the given sequence.

• Then consider the next number,i.e.68.

             Let us consider the number 19 which is the next lowest odd number to 21.

             Taking square on the number 19.

               We have,$19^{2}=361$

               Adding 361 to 68, we have

               $68+361=429$      

          We get the answer as 429, which is the third number in the given sequence.

• Then consider the next number, i.e.429.              

              Let us consider the number 17 which is the next lowest odd number to 19.            

             Taking square on the number 17.

               We have,$17^{2}=289$

               Subtracting 289 from 429, we have

               $429-289=140$

        We get the answer as 140, which is the fourth number in the given sequence.

• Then consider the next number, i.e.140.  

           Let us consider the number 15 which is the next lowest odd number to 15.

            Taking square on the number 15

             We have, $15^{2}=225$.      

             Adding 225 to 140, we have  

           $140+225=365$

We get the answer as 365, which is the fifth number in the given sequence.

• Then consider the next number, i.e.365.  

          Let us consider the number 13 which is the next lowest odd number to 15.            

         Taking square on the number 15.  

         We have,$13^{2}=169$  

         Subtracting 169 from 365, we have

         $365-169=196$

We get the answer as 196, which is the sixth number in the given sequence.    

Thus we understood that the given sequence is achieved by squaring an odd number and subtracting that number from the first number from the sequence. The next number is got by squaring an odd number lower next to the first odd number and adding that number to the second number in the sequence. This procedure is repeated and the sequence is formed.