An algebra problem by Cameron CHang

Algebra Level 3

What is the sum of this arithmetic sequence?

10+100+190....+9010


The answer is 455510.

Cameron CHang by Cameron CHang , 19, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

d = 100 − 10 = 190 − 100 = 90 d=100-10=190-100=90

a n = a 1 + ( n − 1 ) d a_n=a_1+(n-1)d , we substitute

9010 = 10 + ( n − 1 ) ( 90 ) 9010=10+(n-1)(90) ⟹ \implies 9010 = 10 + 90 n − 90 9010=10+90n-90 ⟹ \implies n = 101 n=101

s = n 2 ( a 1 + a n ) = 101 2 ( 10 + 9010 ) = 455510 s=\dfrac{n}{2}(a_1+a_n)=\dfrac{101}{2}(10+9010)=\boxed{455510}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...