What is the explicit formula for the arithmetic sequence -7.5, -9, -10.5, -12, ? O an=-7.5+(-1.5)(n-1) O a,=-7.5+ d(-1.5-1) o

[tex]a_{n}[/tex] = - 1.5n - 6

Step-by-step explanation:

Given that the sequence is arithmetic with n th term ( explicit formula

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 7.5 and d = - 9 - (- 7.5) = - 9 + 7.5 = - 1.5

[tex]a_{n}[/tex] = - 7.5 - 1.5(n - 1) = - 7.5 - 1.5n + 1.5 = - 1.5n - 6

the explicit formula for the arithmetic sequence is given by:

where,

is the first term

d is the common difference,

n is the number of terms.

as per the statement:

–7.5, –9, –10.5, –12,

this is an arithmetic sequence with first term

and d = -1.5

since,

-.5) = -9+7.5 = -1.5,

-10.) = -10.5+9 = -1. and so on

substitute these given values we have;

⇒

therefore, the   explicit formula for the arithmetic sequence is,

a(n) = -7.5 - 1.5(n - 1)

Term 1: -7.5 > -7.5 + 1.5(0)term 2: -9.0 > -7.5 -1.5(1)term 3: -10.5 > -7.5 - 1.5(2)term 4: -12.0 > -7.5 - 1.5(3)the numbers in bracket = n-1explicit formula: f(n) = -7.5 - 1.5(n-1)