the first four terms of an arithmetic sequence are -11, -5, 1, 7. what is the equation for $a_n$? a $a_n =…

the first four terms of an arithmetic sequence are -11, -5, 1, 7. what is the equation for $a_n$? a $a_n = -11(n - 1) - 6$ b $a_n = 6(n - 1) - 11$ c $a_n = -11(n - 1) + 6$ d $a_n = -6(n - 1) - 11$

the first four terms of an arithmetic sequence are -11, -5, 1, 7. what is the equation for $a_n$? a $a_n = -11(n - 1) - 6$ b $a_n = 6(n - 1) - 11$ c $a_n = -11(n - 1) + 6$ d $a_n = -6(n - 1) - 11$

Answer

Explanation:

Step1: Recall arithmetic sequence formula

The formula for the ( n )-th term of an arithmetic sequence is ( a_n = a_1 + (n - 1)d ), where ( a_1 ) is the first term and ( d ) is the common difference.

Step2: Identify ( a_1 ) and ( d )

From the sequence (-11, -5, 1, 7), the first term ( a_1=-11 ). The common difference ( d=-5 - (-11)=6 ) (or ( 1 - (-5)=6 ), etc.).

Step3: Substitute into the formula

Substitute ( a_1 = -11 ) and ( d = 6 ) into ( a_n = a_1 + (n - 1)d ). We get ( a_n=-11+(n - 1)\times6 ), which can be rewritten as ( a_n = 6(n - 1)-11 ).

Answer:

B. ( a_n = 6(n - 1)-11 )