An amphitheater has 50 rows of seats with 30 seats in the first row, 32 in the second, 34 in the third, and so on. Find the total number of seats for all U2 fans for the upcoming U2 concert.
(make sure to count u2lover in the 1st row
This is an A.P. series
Sum of n terms = n/2(2a + (n-1)d
= 50/2(2*30 + 49*2)
what's d? and what's A.P. series? is the latter Arithm. progression?
Yes. A.P. is the arithmetic progression
a - first term
n - #terms
d - difference between any two consecutive terms.
If first term is a, then nth term is: a + (n-1)d
Sum of n terms = n/2(2a + (n-1)d)
It can be easily derived.
(a1 + a2 .. + an)/n = mean
a1 + a2 .. +an = mean*n
In any A.P. mean of n terms = mean of first and last
mean = (a + a + (n-1)d)/2
sum = n/2(2a+(n-1)d)