It is not clear what numbers are represented by the alphabetic characters that appear in the sequence in the question.
2 11 4 10 6 9 8 8 10 7
Steps: 1] Start 2] Initialize double sum=0,x,i,j,y,z=1,a,f=1,k=1; 3] Enter x //ie: The range of sin series 4] Read x 5] Repeat steps 6 to 11 for(i=1 to i<=x) 6] Set j=z=1 7] Repeat steps 8 while(j<=i) 8] Set z=z*i;j=j+1; 9] Repeat steps 10 while(k<=i) 10] Set f=f*k;k=k+1; 11] set a=z/f;sum=sum+a; 12] Display sum 13] Stop
(Assuming 100 is 100 degrees)cos 100 degrees is equal to - sin 10 degrees.In radians, this is - sin (pi/18).Approximating pi as 22/7, this is - sin (11/63)Using four terms of a Taylor series, this is approximately:- (11/63) + (11/63)^3 /6 - (11/63)^5 / 120 + (11/63)^7 / 5040.- (11/63) + (11^3/63^3) /6 - (11^5/63^5) / 120 + (11^7/63^7) / 5040.Rewriting the fractions with the common denominator 63^7:- (11*63^6/63^7) + (11^3*63^4/63^7) /6 - (11^5*63^2/63^7) / 120 + (11^7/63^7) / 5040.Rewriting again with common denominators of 5040:- 5040*(11*63^6/63^7)/5040 + 840*(11^3*63^4/63^7)/5040 - 42*(11^5*63^2/63^7) / 5040 + (11^7/63^7) / 5040.Now add it all up:[- 5040*11*63^6 + 840*11^3*63^4 - 42*11^5*63^2 + 11^7] / (5040*63^7)Now, some seriously long multiplication gives:(- 3466302962466960 + 17612440516440 - 26846879598 + 19487171) / 19852462421401680Some really easy addition:-3448717349342947 / 19852462421401680And finally, do the long division:-0.17371735939 ... and so on.The actual value is -0.17364817766693034885171662676931So, I got 3 decimal places right. Maybe use a better approximation of pi (like 355/113) and more terms of the Taylor series. But you get the picture.
10 square, 11 will ensure you have enough.
tan(11o) = 0.19438 =======
the answer is 1
What would be the next number in this series 15 12 13 10 11 8?
11 comes next.
13
59 is the next number in this series.
10 4 3 11 15 9 8 16 20....
The next number in the series is 67.
11
2
The pattern is - 5 then +2. 2 and 4 are the next numbers in the series.
11 because 4+1=5 3+5=8 2+8=10 1+10=11 0+11=11
12,7,13,8 etc