16. Find the formula for the nth (2017th) term of an arithmetic sequence whose c

Question

16. Find the formula for the nth (2017th) term of an arithmetic sequence whose common difference is 10 and whose first term is 0 a. 2017 b. 2000 c. 2018 d. 20170 e. None of the above 17. An arithmetic sequence the common difference 10, the first term 0 and the last term 1970. The sum of the first 2017 terms of this series is: a. 2017 b. 1008.5 c. 20,000,000 d. 2,000,000,000,000,000 e. None of the above 18. An imaginary number is expressed in cartesian coordinates as z 3vi+4vj. This complex number can be written: a. Z-4expiarctan(4/3)-Z-4expi(tan (4/3)) b. Z=4expiarctan(-43)-Z-4expi(tani(-4/3)) c· z-4expiarctan(5/3)-Z-4expitan"(53)) d. Z-4expiarctan(5/4) Z-4expi(tan (5/4)) ere arctan-tan is the inverse tan function 19. Assume to complex numbers, zi-riexpi and z-rexpi02. Assuming that n>1 and m>1 the complex number z"zz" can be written as: a. rrexpi(0+02) d. e. riF2"cxpi(m@i.n:02) none of the above 20. DeMoivre formula allows the calculation of the roots of complex numbers, z-rexpie where gin can be written as (for n> 1 and k=1, 2, n-1, n): a. z-r[sin((0+360k)n)-icos((0+360k)Vn)] b. z-r"[cos((0+360k) n)-isin((0+360k)Vn) c. z-rt[ cos (0+360k)n)+isin((+360k)/n)] d. z-r[cos((0+360k) n)sin((0+360k)/n)] e. None of the above

Explanation / Answer

16. Nth term= a+(n-1)d, ; a is the first term,d is the common difference. 20 17th term= 0+ (2017-1)10= 20160,henice of the above.

17. Sum of 2017 terms= n/2 [2a+ (n-1)d]= 2017/2 (2016×10)

2017×2016×5= 20,331,360. Hence none of the above.

19.z1n z2m= r1n r2m e (theta1n+theta2m)i

none of the above.

20. Z1/n= r1/n (cos (theta/n)+ iSin ( theta/n)

And using trigonometric tables,we get cos(theat/n) =

cos( (theta+360k)/n) and same is true for sin

Thus option C.

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