An algebra problem by Jimmy PrevailLone

Algebra Level 1

The sum of first 25 25 terms of an arithmetic sequence is 500 500 . If the 2 5 t h 25^{th} term is 32 32 , what is the sum of the first 5 5 terms of the same sequence?

75 50 120 100

Jimmy PrevailLone by Jimmy PrevailLone , 23, Thailand

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1 solution

Filly Mare
Jun 26, 2014

S n = n 2 ( 2 a + ( n − 1 ) d ) S_n=\frac{n}{2}(2a+(n-1)d) and x n = a + ( n − 1 ) d x_n=a+(n-1)d So S 25 = 25 2 ( 2 a + 24 d ) = 500 S_{25} =\frac{25}{2}(2a+24d) = 500 and x 25 = a + 24 d = 32 x_{25}=a+24d=32 Multiplying the x 25 x_{25} equation by 25 then subtracting S 25 S_{25} from it makes d=1 and a=8 by simultaneous equations. Sum of 8+9+10+11+12=50

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