Use the equation an = a1 + (n – 1)d to write a rule for the arithmetic sequence 32, 41, 50, . …

The common difference is 9.
an = 9n + 9
an = 9n + 23
an = 9n + 32
an = 9n + 1

an = 9n + 23

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a1 + (n - 1)d

Where

a1 represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 32

d = 9

Therefore, the equation or rule for the given arithmetic sequence would be

an = 32 + (n - 1)9

Expanding the brackets, it becomes

an = 32 + 9n - 9

an = 9n + 32 - 9

an = 9n + 23

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step-by-step explanation:

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2