Chindayidn
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Find the sum of all even integers from 30 to 101834 by using the formula Sn=a sub1 +(a1+d)+(a1+3d)+...+[a1+(n-1)d]

Sagot :

Mlcparra16idn
Please note the following: 1st term=30, nth term=101834, d=2

[tex]S_n=a_1+(a_1+d)+(a_1+2d)+...+[a_1+(n-1)d] \\ =a_1n+ \frac{n(n-1)d}{2} \\ = \frac{2a_1+n(n-1)d}{2} \\ =\frac{n(2a_1+(n-1)d)}{2} \\ = \frac{n(a_1+a_n)}{2} [/tex]

[tex]n= \frac{a_n-a_1}{d} +1= \frac{101834-30}{2} +1=50903[/tex]

[tex]S_n= \frac{50,903(30+101,834)}{2} = \frac{50,903(10,1864)}{2} =2,592,591,596[/tex]