Question

NO LINKS!! URGENT HELP PLEASE!!!

Given the explicit formula for a geometric sequence find the first five terms and the 8th term.

36. a_n = -3^(n-1)

37. a_n = 2 * (1/2)^(n - 1)

Answer 1

see explanation

Explanation:

to find the first 5 terms substitute n = 1, 2, 3, 4, 5 into the explicit formula

36

a₁ = -
`3^(1-1)` = -
`3^(0)` = - 1 [
`a^(0)` = 1 ]

a₂ = -
`3^(2-1)` = -
`3^(1)` = - 3

a₃ = -
`3^(3-1)` = - 3² = - 9

a₄ = -
`3^(4-1)` = - 3³ = - 27

a₅ = -
`3^(5-1)` = -
`3^(4)` = - 81

the first 5 terms are - 1, - 3, - 9, - 27, - 81

to find a₈ substitute n = 8 into the explicit formula

a₈ = -
`3^(8-1)` = -
`3^(7)` = - 2187

37

to find the first 5 terms substitute n = 1, 2, 3, 4, 5 into the explicit formula

a₁ = 2 ×
`((1)/(2)) ^(1-1)` = 2 ×
`((1)/(2)) ^(0)` = 2 × 1 = 2

a₂ = 2 ×
`((1)/(2)) ^(2-1)` = 2 ×
`((1)/(2)) ^(1)` = 2 ×
`(1)/(2)` = 1

a₃ = 2 ×
`((1)/(2)) ^(3-1)` = 2 ×
`((1)/(2)) ^(2)` = 2 ×
`(1)/(4)` =
`(1)/(2)`

a₄ = 2 ×
`((1)/(2)) ^(4-1)` = 2 × (
`(1)/(2)` )³ = 2 ×
`(1)/(8)` =
`(1)/(4)`

a₅ = 2 ×
`((1)/(2)) ^(5-1)` = 2 ×
`((1)/(2)) ^(4)` = 2 ×
`(1)/(16)` =
`(1)/(8)`

the first 5 terms are 2 , 1 ,
`(1)/(2)` ,
`(1)/(4)` ,
`(1)/(8)`

to find a₈ substitute n = 8 into the explicit formula

a₈ = 2 ×
`((1)/(2)) ^(8-1)` = 2 ×
`((1)/(2)) ^(7)` = 2 ×
`(1)/(128)` =
`(1)/(64)`

Answer 2

The explicit formula for a geometric sequence is:

a_n = a_1 * r^(n - 1)

where:

• a_n is the nth term in the sequence
• a_1 is the first term in the sequence
• r is the common ratio between the terms in the sequence

In equation 36,

we can see that the first term is -3 and the common ratio is -3. Therefore, we can write the explicit formula for this sequence as:

a_n = -3 * (-3)^(n - 1)

Using this formula, we can find the first five terms and the 8th term in the sequence:

a_1 = -3

a_2 = -3 * (-3) = 9

a_3 = -3 * (-3)^2 = -27

a_4 = -3 * (-3)^3 = 81

a_5 = -3 * (-3)^4 = -243

a_8 = -3 * (-3)^7 = 6561

In equation 37,

we can see that the first term is 2 and the common ratio is 1/2. Therefore, we can write the explicit formula for this sequence as:

a_n = 2 * (1/2)^(n - 1)

Using this formula, we can find the first five terms and the 8th term in the sequence:

a_1 = 2

a_2 = 2 * (1/2) = 1

a_3 = 2 * (1/2)^2 = 1/2= 0.5

a_4 = 2 * (1/2)^3 =1/4= 0.25

a_5 = 2 * (1/2)^4 = 1/8=0.125

a_8 = 2 * (1/2)^7 = 1/64=0.015625