In an increasing sequence of 10 consecutive integers the sum of the first 5 integers in 560. What is the sum of the last 5 integers in the sequence?
now the approach given in the answer is fairly straightforward, saying that sum of first five integers from x,x+1,x+2,x+3 & x+4 gives us the equation 5x+10=560,thus 5x=550 and x=110.
However when i tried to do it on my own i applied the formula for the sum of an Arithmetic Progression which is:
(2x+(n-1)d)*n/d
where x is the first term of the A.P., n is the number of terms, and d is the difference b/w terms.
when applying this formula you end up with,
(2x+(5-1)1)*5/1=560
-> 2x+4=112
-> x=108/2 which equals 54
am i making some really silly mistake here? is the formula wrong? (i rechecked it in a couple of places)... does it not apply for consecutive numbers? Conceptually the answer is obviously wrong as 5 consecutive numbers adding to over 500 means each must be greater than 100 but i can't seem to see the mistake i'm making...
now the approach given in the answer is fairly straightforward, saying that sum of first five integers from x,x+1,x+2,x+3 & x+4 gives us the equation 5x+10=560,thus 5x=550 and x=110.
However when i tried to do it on my own i applied the formula for the sum of an Arithmetic Progression which is:
(2x+(n-1)d)*n/d
where x is the first term of the A.P., n is the number of terms, and d is the difference b/w terms.
when applying this formula you end up with,
(2x+(5-1)1)*5/1=560
-> 2x+4=112
-> x=108/2 which equals 54
am i making some really silly mistake here? is the formula wrong? (i rechecked it in a couple of places)... does it not apply for consecutive numbers? Conceptually the answer is obviously wrong as 5 consecutive numbers adding to over 500 means each must be greater than 100 but i can't seem to see the mistake i'm making...
