Question

A sequence can be generated by using an=4an−1 where a1=6 (a) 6, 20, 76, 300 (b)6, 24, 96, 384 (c)6, 10, 14, 18 (d) 6, 20, 100, 500

Answer 1

Answer:

• Option (b) 6, 24, 96, 384

Explanation:

The complete question is:

A sequence can be generated by using    $a_n=4a_{(n-1)}$    where    $a_1=6$     and n is a whole number greater than 1. What are the first four terms in the sequence.

The given rule     $a_n=4a_{(n-1)}$     is a recursive formula, which means that  to find any term consecutive term, from the second one, you multiply the current term by 4.

Thus:

$a_1=6\\ \\ a_2=4a_1=4\times 6=24\\\\ a_3=4a_2=4\times 24=96\\ \\ a_4=4a_3=4\times 96=384$

Answer 2

Answer:

The option (b) is correct as the sequence is generated as 6, 24, 94, 384,...

Step-by-step explanation:

Considering the sequence

$a_{n} =4a_{n-1}$

As $a_{1} =6$

So,

$a_{n} =4a_{n-1}$

$a_{2} =4a_{2-1}$

$a_{2} =4a_{1}$

$a_{2} =4.6$

$a_{2} =24$

$a_{3} =4a_{3-1}$

$a_{3} =4a_{2}$

$a_{3} =4.24$

$a_{3} =96$

$a_{4} =4a_{4-1}$

$a_{4} =4a_{3}$

$a_{4} =4a_{3}$

$a_{4} =4.96$

$a_{4} =384$

Therefore, the option (b) is correct as the sequence is generated as 6, 24, 94, 384,...

Keywords: sequence

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