The Correct answer is C) the summation from n equals one to 6 of quantity negative 7 minus 3 times n
Step-by-step explanation:
The given Arithmetic sequence: −10, −13, −16, …
Theory : For arithmetic sequence : a, a+d,a+2d......a+(n-1)d
Formula for summation is given as Sn = [tex]\sum\limits^{n=N}_{n=1} {a+(N-1)d}[/tex]
Where, a= First term of sequence = (-10) and d= difference of any two consecutive terms = (a+d)-(a) = (-13)-(-10)= (-3)
Putting values in Summation formula
Sn = [tex]\sum\limits^{n=N}_{n=1} {a+(N-1)d}[/tex]
Sn = [tex]\sum\limits^{n=6}_{n=1} {(-10)+(N-1)(-3)}[/tex]
Sn = [tex]\sum\limits^{n=6}_{n=1} {(-10) -3N+3)}[/tex]
Sn = [tex]\sum\limits^{n=6}_{n=1} {(-7-3N)}[/tex]
Thus, Correct answer is C) the summation from n equals one to 6 of quantity negative 7 minus 3 times n
