Question

51,55,71,107,171,? what is the value come on the place of ? ​

Answer 1

Answer:

271

Step-by-step explanation:

51      55        71        107        171

51   (51+4)  (55+16)  (71+36)  (107+64)

51   (51+2²)  (55+4²)  (71+6²)  (107+8²)

         Hence, we can say,

nth term after 51, is defined by (n - 1)th term + (2n)².

 Thus,

next term = 171 + (10)²

                = 171 + 100

                = 271

If the above, looks peculiar, either use desktop mode, or see below, I have added that below,

 *   51  = 51 + 0    = 51 + 0²

 *   55 = 51 + 4    = 51 + 2²

 *   71  = 55 + 16  = 55 + 4²

 *  107 = 71 + 36  = 71 + 6²

 *  171  = 107 + 64= 107 + 8²

Next number to be squared should be next even number = 10. And the number that will be added is 171.

So, next number is to be 171 + 10² =  171 + 100 = 271