Question: How many terms of the A.P. \begin{align} -6, -\frac{11}{2}, -5, ... \end{align} are needed to give the sum –25?

Answer:

Let the sum of n terms of the given A.P. be –25.

It is known that, \begin{align} S_n = \frac {n}{2}\left[2a + (n -1)d\right]\end{align}, where n = number of terms, a = first term, and d = common difference

Here, a = –6

\begin{align} d = -\frac{11}{2} + 6 = \frac{-11 + 12}{2} = \frac{1}{2}\end{align}

Therefore, we obtain

\begin{align} -25 = \frac {n}{2}\left[2 × (-6) + (n -1)×\frac{1}{2}\right]\end{align}

\begin{align} => -50 = n\left[-12 + \frac{n}{2} - \frac{1}{2}\right]\end{align}

\begin{align} => -50 = n\left[-\frac{25}{2} + \frac{n}{2}\right]\end{align}

\begin{align} => -100 = n\left(-25 + n\right)\end{align}

\begin{align} => n^2 - 25n + 100 = 0\end{align}

\begin{align} => n^2 - 5n -20n + 100 = 0\end{align}

\begin{align} => n(n - 5)- 20(n - 5) = 0\end{align}

\begin{align} => n = 20 \; or\; 5\end{align}

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

< Previous Question

Next Question >

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='2' AND subId='6' AND ex_no!=0 AND status=1 and id!=1000 ORDER BY views desc, last_viewed_on desc limit 0,10

Popular questions of class 11 Mathematics

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Q: Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Q: Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='2' AND subId='6' AND ex_no!=0 AND status=1 and id!=1000 ORDER BY last_viewed_on desc limit 0,10

Recently Viewed Questions of Class 11 Mathematics

Prove the following by using the principle of mathematical induction for all n ∈ N:

n (n + 1) (n + 5) is a multiple of 3.

Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Let the sum of n, 2n, 3n terms of an A.P. be S₁, S₂ and S₃, respectively, show that S₃ = 3 (S₂– S₁)

Q: Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:
(i) 5__A
(ii) 8__A
(iii) 0__A
(iv) 4__A
(v) 2__A
(vi) 10__A

A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Question: How many terms of the A.P. \begin{align} -6, -\frac{11}{2}, -5, ... \end{align} are needed to give the sum –25?

< Previous Question

Next Question >

Popular questions of class 11 Mathematics

Recently Viewed Questions of Class 11 Mathematics

Comments

Comment(s) on this Question

NCERT Solutions

Quick Links

Resources

Support