Advertisements
Advertisements
प्रश्न
How many terms of the A.P. -6 , `-11/2` , -5... are needed to give the sum –25?
Advertisements
उत्तर
Let the sum of n terms of the given A.P. be –25.
संबंधित प्रश्न
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
Find the sum of the following serie:
(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of all integers between 84 and 719, which are multiples of 5.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
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 first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
If a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 are in A.P.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
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.
Write the common difference of an A.P. the sum of whose first n terms is
If Sn denotes the sum of first n terms of an A.P. < an > such that
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
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =
Mark the correct alternative in the following question:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.
If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
