How many terms of the series 54 51 48

Asked by admin @ 13/08/2021 in Math viewed by 261 People

How many terms of series 54,51,48,....be taken so that their sum is 513? explain the double answer.

Answered by admin @ 13/08/2021

Use forumla ,
Sn=n/2{2a+(n-1)d}

from series ,
a=54
d=-3
Sn=513
now,
513=n/2{54 x 2+(n-1)(-3)}
1026=n{108+3-3n}
=111n-3n^2

3n^2-111n+1026=0

n^2-37n+342=0

use quadratic formula ,
n={37+_√(1369-1368)}/2
=(37+_1)/2=19 and 18
here we see n gain 2 value e.g 19 and 18
now, we check it
18th term=54+(17)(-3)=54-51=3
19th term =54-18 x 3=0
you also see 19th term is zero
so adding or no adding 19th term value of sum is always 513
so , n gain two values

Brad is testing whether school is more enjoyable when students are making high grades. he asked 110 students if they enjoyed school and whether their gpa was above or below 3.5. he found that 38 of the 45 students with a gpa above 3.5 reported that they enjoyed school, and 7 of the 65 students with a gpa below 3.5 reported that they enjoyed school. what is the probability that a student with a gpa below 3.5 does not enjoy school?

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 623 persons

What is the sum of the first seven terms of the geometric series? 3 + 12 + 48 + 192 + ...

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 333 persons

What is the sum of the first seven terms of the geometric series? 3 + 12 + 48 + 192 + ...

Match the logical fallacy to the correct definition. match term definition ----incorrectly assumes that one event causes another a) fear claims that one -------action leads to a series of undesirable events b) false dichotomy claims ---------something is true because most people agree c) slippery slope appeals to ------the desire to be safe d) popularity gives two choices, one of which is not -------truly an option e) post hoc

Asked by maham237 @ 13/01/2021 in English viewed by 528 persons

In selecting a target market for a banks checking accounts, the banks marketers should consider the banks strengths, who would get the most value from those strengths, and ____. a- the cost of reaching different segments b- the roles in the banks buying center c- whether to enter new markets or develop new products d- the lifestyle me of the banks employees

Asked by maham237 @ 14/01/2021 in Business viewed by 336 persons

Match the literary term with the definition. 1. dynamic character a character who encounters conflict and is changed by it and exhibits multiple traits 2. flat character a character who grows and changes as a result of the plot 3. round character a character who shows only one or two personality traits and does not undergo substantial growth or change through the course of the story 4. static character a character who remains constant in his or her beliefs, attitudes, behaviors, and personality

Asked by maham237 @ 10/01/2021 in World Languages viewed by 620 persons

Which population is most likely to have exponential growth? a. the mice living in a meadow with plenty of predators and limited food b. the mice living in a house with plenty of food and no predators c. the fish living in a coral reef where there are many sharks d. the fish living in a pond where many humans fish

Asked by maham237 @ 13/01/2021 in Biology viewed by 322 persons

Find the first three terms of each arithmetic series calculator

Asked by admin @ 29/10/2021 in Mathematics viewed by 320 persons

Write the first five terms of a sequence. Write both an explicit formula and a recursive formula for a general term in the sequence. recursive formula for arithmetic sequence recursive …