Question
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.
Answers
Reiny
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
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
Hnin
which term of the progression 19+181/5+17 2/5+...is the first negative lterm?which is the smallest number of terrms which must be taken for their sum to be negative?Calculate this sum exactly.
Anonymous
Please give the second part of question with complete solution
Anonymous
Solve the second part
queentosleet
FIND CONSECUTIVE COUNTING NUMBERS WHOSE SUM IS 50.
FIND THE SUM.
19+ 18
how u do this help
FIND THE SUM.
19+ 18
how u do this help
Anonymous
thank you
prasha
thanks now i know how to solve this