Question 631827
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Hi,
Arithmetic sequence
In General: {{{a[n]=a[1]+(n-1)*d}}}  and {{{S[n]=(n/2)(2*a[1]+ (n-1)d)}}}
{2, 4, 6, 8, ..., 70) d = 2  and {{{2 +(n-1)*2 = 70}}} n = 35
finding the Sum of the first 35 Terms: {{{S[35]=(35/2)(2*2+ 34*2) = (35/2)*72 = 1260 }}}
14, 8, 2,...; n=9   d = -6
finding the Sum of the first 9 Terms:{{{S[9]=(9/2)(2*14+ (8)*-6) = (9/2)(-20) = -90}}}

Geometric sequence
In General: {{{a[n] = a[1]*r^highlight((n-1))}}}   and {{{S[n]= a[1]((1-r^n)/(1-r))}}}
Find the sum of the geometric sequence 42, 7, 7/6, .... , {{{highlight(42(1/6) ^8)}}} {{{r = 1/6}}} and last term is the 9th Term
finding the Sum of the first 9 Terms:{{{S[9]= 42((1-(1/6)^9)/(5/6))}}} using {{{42/(5/6)= 50.4}}} as {{{(1/6)^9}}} is so insignificant
-1, 11, -121, ...; n = 9 , r = -11 :
finding the Sum of the first 9 Terms: {{{S[9]= -1((1-(-11)^9)/(12))}}}
will Let You finish this one out