Which term of the progression 19+ 18 1/5 + 17 2/5 + …is the first negative term? What is the smallest number of terms which must be taken for their sum to be negative ? Calculate this sum exactly.
Arithmetic series with
a = 19
d = -4/5
a + (n-1)d < 0
19 + (n-1)(-4/5) < 0
19 - (4/5)n + 4/5 < 0
times 5
95 - 4n + 4 < 0
-4n < -99
n > 99/4
n > 24.75
so it must be term(25) which is the first one negative.
check:
term(25) = 19 + 24(-4/5) = -1/5
term(24) = 19 + 23(-4/5) = 3/5
OK
use the formula for sum(n) < 0
to do the 2nd part of your problem
thanks now i know how to solve this
Please give the second part of question with complete solution
thank you
FIND CONSECUTIVE COUNTING NUMBERS WHOSE SUM IS 50.
FIND THE SUM.
19+ 18
how u do this help