The 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively. What is the 1st term of the sequence.

If the 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively, then the 1st term of the sequence is -1

The nth term of an arithmetic sequence is given by the formula:

The 8th term of the arithmetic sequence is 20

The 20th term of the arithmetic sequence is 56

Subtract equation (1) from equation (2)

12d  =  36

d  =  36/12

d  =  3

Substitute d = 3 into equation (1)

a  +  7d  =  20

a  +  7(3)  =  20

a  +  21  =  20

a   =  20  -  21

a  =  -1

The first term of the arithmetic sequence is -1

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Step-by-step explanation:

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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