Find the sum of the first 40 terms of the arithmetic sequence 17, 24, 31,

The sum of the first 40 terms of 17, 24, 31, 38,..., with a common difference of 7 is: 6,140.

Recall:

Thus, the first term of the sequence, 17, 24, 31, 38,..., is: 17

Common difference (d) = 38 - 31 = 31 - 24 = 24 - 17 = 7

Plug in the values into the formula for finding the sum of the first n terms:

Therefore, the sum of the first 40 terms of 17, 24, 31, 38,..., with a common difference of 7 is: 6,140.

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6120

Step-by-step explanation:

First let's calculate the 40th term.  Here a(n) = 17+7(n-1), so a(40) = 17 + 7(39).  This works out to 290.

To find the sum of the first 40 terms, add together the first and last terms and then divide the result by 2 (which gives us the average of the first and last terms), and then mult. this result by 40, the number of terms:

40(17 + 290)/2 = 40(306)/2 = 6120

answer: 1 and 3

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