Arith Prog problem

[raunakrajan]

If a sequence of 8 consecutive odd integers with increasing values has 9 as the 7th term what is the sum of the terms in the sequence?

thanks!

[amising6]

If a sequence of 8 consecutive odd integers with increasing values has 9 as the 7th term what is the sum of the terms in the sequence?

thanks!
soln:
we know number of the form 2n+1 is odd
funda out here will be to choose odd number in such a way that it helps in solving:
2n-1 ,2n-3,2n-5 (subtracting 2 from 2n+1 will result in odd number)
2n+3,2n+5, will be odd
so 8 consecutive odd numbers will be 2n-7,2n-5,2n-3,2n-1,2n+1,2n+3,2n+5,2n+7
now 7th term is 2n+5 ie given as 9
2n+5=9 solving we get n as 2
replacing n=2 n series we will get
series =-3,-1,1,3,5,7,9,11
sum=32
now

[Stuart@KaplanGMAT]

If a sequence of 8 consecutive odd integers with increasing values has 9 as the 7th term what is the sum of the terms in the sequence?

thanks!

Amising's solution is correct, but far more work that you'd want to do on the actual GMAT. Remember, no points on test day for extra work!

If we know that the 7th term is 9, we can simply plot out the entire set:

after 9 we have one term: 11

before 9 we have six terms (counting backwards): 7, 5, 3, 1, -1, -3

So, our full set is:

{-3, -1, 1, 3, 5, 7, 9, 11, 13}

We want the sum... the first 4 terms cancel out, leaving us with:

5+7+9+11 = 32