Question

NO LINKS!! Write the first 5 terms of the geometric sequence

a1 = 6, r = 4

a1=
a2=
a3=
a4=
a5=

Answer 1

Explanation:

since it is geometric sequence we will use the formula

`tn = {ar}^(n - 1)`

a = 6

r = 4

The first term

T1(a) = 6

The second term

`t2 = {a * r}^(2 - 1)`

`t2 = {6 * 4}^(1 ) = 24`

The Third Term

`t3 = {a * r}^(3 - 1) = {a * r}^(2)`

`t3 = {6 * 4}^(2) = 6 * 16 = 96`

The fourth term

`t4 = {a * r}^(4 - 1) = {a * r}^(3)`

`t4 = {6 * 4}^(3) = 6 * 64 = 384`

The fifth term

`t5 = {a * r}^(5 - 1) = {a * r}^(4)`

`t5 = {6 * 4}^(4) = 6 * 256 = 1,536`

i hope these helped

Answer 2

6, 24, 96, 384, 1536, ...

Explanation:

`\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^(n-1)$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}`

Given:

• a = 6
• r = 4

Substitute the given values of a and r into the formula to create an equation for the nth term:

`a_n=6(4)^(n-1)`

To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.

`\begin{aligned}\implies a_1&=6(4)^(1-1)\\&=6(4)^(0)\\&=6(1)\\&=6\end{aligned}`

`\begin{aligned}\implies a_2&=6(4)^(2-1)\\&=6(4)^(1)\\&=6(4)\\&=24\end{aligned}`

`\begin{aligned}\implies a_3&=6(4)^(3-1)\\&=6(4)^(2)\\&=6(16)\\&=96\end{aligned}`

`\begin{aligned}\implies a_4&=6(4)^(4-1)\\&=6(4)^(3)\\&=6(64)\\&=384\end{aligned}`

`\begin{aligned}\implies a_5&=6(4)^(5-1)\\&=6(4)^(4)\\&=6(256)\\&=1536\end{aligned}`

Therefore, the first 5 terms of the given geometric sequence are:

• 6, 24, 96, 384, 1536, ...