Question

NO LINKS!! Write an expression for the nth term of the geometric sequence. Then find the indicated term.

a1= 3, r = √(2), n = 10

a_n =
a_10=

Answer 1

`a_n=3\left(√(2)\right)^(n-1)`

`a_(10)=48 √(2)`

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 = 3`
• 
  `r = √(2)`
• 
  `n=10`

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

`a_n=3\left(√(2)\right)^(n-1)`

To find the 10th term, substitute n = 10 into the equation:

`\implies a_(10)=3\left(√(2)\right)^(10-1)`

`\implies a_(10)=3\left(√(2)\right)^(9)`

`\implies a_(10)=3 \cdot 2^{(9)/(2)}`

`\implies a_(10)=3 \cdot 2^{4+(1)/(2)}`

`\implies a_(10)=3 \cdot 2^(4) \cdot 2^{(1)/(2)}`

`\implies a_(10)=3 \cdot 16 \cdot √(2)`

`\implies a_(10)=48 √(2)`

Answer 2

`tn = {3 * √(2) }^(n - 1)`

Explanation:

since it is geometric sequence we will use the formula

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

n = 10

r = √2

a = 3

lets first see the result of the 10th term

`t10 = {ar}^(10 - 1)`

`t10 = {ar}^(9)`

`t10 = {3 * √(2) }^(9)`

t10 = 3 × 22.63

t10 = 67.89

approximately 68

t10 = 68

for the nth term

Tn = ar^n–1

`tn = {3 * (√(2) })^(n - 1)`

i hope this helps