Question

the next term in the following pattern is 49,925,2549,49121,121169​

Answer 1

Answer:

49121 is ur answer

Explanation:

49 = 2² -3²

925 = 3² - 5²

2549 = 5² - 7²

49121 = 7² - 11²

121169 = 11² - 13²

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Answer 2

The next pattern 49 , 925 , 2549 , 49121 , 121169 is 169289

Given :

The pattern 49 , 925 , 2549 , 49121 , 121169

To find :

The next term in the pattern

Solution :

Step 1 of 2 :

Write down the given seris

The given series

49 , 925 , 2549 , 49121 , 121169

Step 2 of 2 :

Find the pattern

1st term = 49 = 2²3²

2nd term = 925 = 3² 5²

3rd term = 2549 = 5²7²

4th term = 49121 = 7² 11²

5th term = 121169 = 11² 13²

Thus we see that nth term of the sequence is of the form a²b² when a is nth prime number and b is (n+1)th prime number

Step 3 of 3 :

Find the next term

We have to find the 6th term of the sequence

6th prime number = 13

7th prime number = 17

Hence the required next term

= 6th term of the sequence

= 13² 17²

= 169289

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