Question

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

a1 = 2, r = -1/4

a1=
a2=
a3=
a4=
a5=

Answer 1

Explanation:

since it is geometric sequence we will use the formula

`tn = {a * r}^(n - 1)`

a = 2

`r = - (1)/(4)`

The first term

T1(a) = 2

The second Term

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

`t2 = {2 * - (1)/(4) }^(1) = - (1)/(2)`

The third term

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

`t3 = {2 * - (1)/(4) }^(2) = 2 * - (1)/(16) = (1)/(8)`

The fourth term

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

`t4 = {2 * - (1)/(4) }^(3) = 2 * - (1)/(64) = - (1)/(32)`

The fifth term

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

`t5 = {2 * - (1)/(4) }^(4) = 2 * - (1)/(256) = - (1)/(128)`

i hope all these helped

Answer 2

`2,\; -(1)/(2),\; (1)/(8),\; -(1)/(32),\; (1)/(128)`

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=2`

• 
  `r=-(1)/(4)`

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

`a_n=2\left(-(1)/(4)\right)^(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 & =2\left(-(1)/(4)\right)^(1-1)\\& =2\left(-(1)/(4)\right)^(0)\\& =2\left(1\right)\\&=2\end{aligned}`

`\begin{aligned}\implies a_2 & =2\left(-(1)/(4)\right)^(2-1)\\& =2\left(-(1)/(4)\right)^(1)\\& =2\left(-(1)/(4)\right)\\&=-(1)/(2)\end{aligned}`

`\begin{aligned}\implies a_3 & =2\left(-(1)/(4)\right)^(3-1)\\& =2\left(-(1)/(4)\right)^(2)\\& =2\left((1)/(16)\right)\\&=(1)/(8)\end{aligned}`

`\begin{aligned}\implies a_4 & =2\left(-(1)/(4)\right)^(4-1)\\& =2\left(-(1)/(4)\right)^(3)\\& =2\left(-(1)/(64)\right)\\& =-(1)/(32)\end{aligned}`

`\begin{aligned}\implies a_5 & =2\left(-(1)/(4)\right)^(5-1)\\& =2\left(-(1)/(4)\right)^(4)\\& =2\left((1)/(256)\right)\\& =(1)/(128)\end{aligned}`

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

`2,\; -(1)/(2),\; (1)/(8),\; -(1)/(32),\; (1)/(128)`