Question

5. Write the next term of each of the following sequences :
(ii) 6, 9, 16, 27, 42, ...​

Answer 1

Answer:

The next term in the sequence 6, 9, 16, 27, 42, ...​ = 61

Step-by-step explanation:

To find,

The next term in the sequence  6, 9, 16, 27, 42, ...​

Solution:

Second term - first term = 9 - 6 = 3

Third term - second term = 16 -9 = 7

Fourth term - third term = 27 - 16 = 11

Fifth term - fourth term = 42 - 27 = 15

Let us consider the difference between the terms,

The differences are 3,7,11,15,....... this form an AP with common difference 4

The next term in this AP is 15+4 = 19

That is the difference between the fifth term and sixth term in the given sequence  = 19

The sixth term in the sequence  = 42+19 =61

The next term in the sequence 6, 9, 16, 27, 42, ...​ = 61

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