# Find the first six terms of the sequence. {eq}a_1 = -6, a_n = 4 \cdot a_{n - 1} {/eq}

## Question:

Find the first six terms of the sequence.

{eq}a_1 = -6, a_n = 4 \cdot a_{n - 1} {/eq}

## Sequence:

In mathematics, the sequence can be defined as the list of things, objects, or numbers that are in order. Repetitions are allowed in the sequence The sequence is of two types: finite sequence and infinite sequence.

## Answer and Explanation: 1

We are given the following data:

• The first term of the sequence is {eq}{a_1} = - 6 {/eq}.

The expression for the {eq}{n^{{\rm{th}}}} {/eq} term of the sequence is,

{eq}{a_n} = 4 \cdot {a_{n - 1}} {/eq}

The second term of the sequence is,

{eq}\begin{align*} {a_2} &= 4 \cdot {a_{2 - 1}}\\[0.3 cm] &= 4 \times {a_1}\\[0.3 cm] &= 4 \times - 6\\[0.3 cm] &= - 24 \end{align*} {/eq}

The third term of the sequence is,

{eq}\begin{align*} {a_3} &= 4 \cdot {a_{3 - 1}}\\[0.3 cm] &= 4 \times {a_2}\\[0.3 cm] &= 4 \times - 24\\[0.3 cm] &= - 96 \end{align*} {/eq}

The fourth term of the sequence is,

{eq}\begin{align*} {a_4} &= 4 \cdot {a_3}\\[0.3 cm] &= 4 \times {a_3}\\[0.3 cm] &= 4 \times - 96\\[0.3 cm] &= - 384 \end{align*} {/eq}

The fifth term of the sequence is,

{eq}\begin{align*} {a_5} &= 4 \cdot {a_{5 - 1}}\\[0.3 cm] &= 4 \times {a_4}\\[0.3 cm] &= 4 \times - 384\\[0.3 cm] &= - 1536 \end{align*} {/eq}

The sixth term of the sequence is,

{eq}\begin{align*} {a_6} &= 4 \cdot {a_{6 - 1}}\\[0.3 cm] &= 4 \times {a_5}\\[0.3 cm] &= 4 \times - 1536\\[0.3 cm] &= - 6144 \end{align*} {/eq}

Thus, the first six terms of the sequence are {eq}\boxed{ - 6,\; - 24,\; - 96,\; - 384,\; - 1536,\; - 6144} {/eq}.