Question

write the first four terms of the sequence
$a_n = 2(n + 1)!$
$a_1 = \square$

Explanation:

Step1: Find \(a_1\)

Substitute \(n = 1\) into \(a_n = 2(n + 1)!\).
\(a_1 = 2(1 + 1)! = 2\times2! = 2\times2 = 4\)

Step2: Find \(a_2\)

Substitute \(n = 2\) into \(a_n = 2(n + 1)!\).
\(a_2 = 2(2 + 1)! = 2\times3! = 2\times6 = 12\)

Step3: Find \(a_3\)

Substitute \(n = 3\) into \(a_n = 2(n + 1)!\).
\(a_3 = 2(3 + 1)! = 2\times4! = 2\times24 = 48\)

Step4: Find \(a_4\)

Substitute \(n = 4\) into \(a_n = 2(n + 1)!\).
\(a_4 = 2(4 + 1)! = 2\times5! = 2\times120 = 240\)

Answer:

The first four terms are \(4\), \(12\), \(48\), \(240\) (with \(a_1 = 4\))