Question

In arithmetic sequence what is the next term of 4,8,20,56?

Answer 1

SOLUTION

CORRECT QUESTION

In the sequence what is the next term of 4 , 8 , 20 , 56

EVALUATION

Here the given sequence is 4 , 8 , 20 , 56

1st term = 4

2nd term = 8

3rd term = 20

4th term = 56

Now

2nd term - 1st term = 8 - 4 = 4 = 4 × 1

3rd term - 2nd term = 20 - 8 = 12 = 4 × 3

4th term - 3rd term = 56 - 20 = 36 = 4 × 9

$\sf Let \: nth \: term = a_n$

$\sf \: a_{n + 1} - a_n = 4 \times {3}^{n - 1} \: \: where \: a_1 = 4$

Hence the required next term

= 5th term

$\sf = a_5$

$\sf = a_4 + 4 \times {3}^{4 - 1}$

$\sf = a_4 + 4 \times {3}^{3}$

$\sf = 56 + 108$$\sf = 164$

FINAL ANSWER

Hence the required next term = 164

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