Question

find the first four terms of the sequence given by the following.
( a_n = -4 cdot 5^{n - 1} ), ( n = 1, 2, 3 dots )

Explanation:

Step1: Find \(a_1\)

Substitute \(n = 1\) into \(a_n=-4\cdot5^{n - 1}\).
\(a_1=-4\cdot5^{1 - 1}=-4\cdot5^{0}=-4\cdot1=-4\)

Step2: Find \(a_2\)

Substitute \(n = 2\) into \(a_n=-4\cdot5^{n - 1}\).
\(a_2=-4\cdot5^{2 - 1}=-4\cdot5^{1}=-4\cdot5=-20\)

Step3: Find \(a_3\)

Substitute \(n = 3\) into \(a_n=-4\cdot5^{n - 1}\).
\(a_3=-4\cdot5^{3 - 1}=-4\cdot5^{2}=-4\cdot25=-100\)

Step4: Find \(a_4\)

Substitute \(n = 4\) into \(a_n=-4\cdot5^{n - 1}\).
\(a_4=-4\cdot5^{4 - 1}=-4\cdot5^{3}=-4\cdot125=-500\)

Answer:

The first four terms are \(-4\), \(-20\), \(-100\), \(-500\)