Advertisements
Advertisements
प्रश्न
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
Advertisements
उत्तर
\[\text { Given: } \]
\[\text{ An } \hspace{0.167em} A . P .\text { with a = - 6 and d }= - \frac{11}{2} - \left( - 6 \right) = \frac{1}{2}\]
\[ S_n = - 25\]
\[ \therefore - 25 = \frac{n}{2}\left[ 2 \times \left( - 6 \right) + \left( n - 1 \right)\frac{1}{2} \right]\]
\[ \Rightarrow - 25 = \frac{n}{2}\left[ - 12 + \frac{n}{2} - \frac{1}{2} \right]\]
\[ \Rightarrow - 50 = n\left[ \frac{n}{2} - \frac{25}{2} \right]\]
\[ \Rightarrow - 100 = n\left( n - 25 \right)\]
\[ \Rightarrow n^2 - 25n + 100 = 0\]
\[ \Rightarrow \left( n - 20 \right)\left( n - 5 \right) = 0\]
\[ \Rightarrow n = 20 \text { or } n = 5\]
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Which term of the A.P. 3, 8, 13, ... is 248?
Is 68 a term of the A.P. 7, 10, 13, ...?
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n terms
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of all integers between 50 and 500 which are divisible by 7.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
a (b +c), b (c + a), c (a +b) are in A.P.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
If x, y, z are in A.P. and A1 is the A.M. of x and y and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.
Write the sum of first n even natural numbers.
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [sec a1 sec a2 + sec a2 sec a3 + .... + sec an − 1 sec an], is
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
Mark the correct alternative in the following question:
If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is
Mark the correct alternative in the following question:
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.
The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.
