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.

APPEARS IN
संबंधित प्रश्न
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.
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5:9. Find the value of m.
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
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.
How many numbers of two digit are divisible by 3?
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
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 :
a + b, a − b, a − 3b, ... to 22 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
Solve:
25 + 22 + 19 + 16 + ... + x = 115
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
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?
If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.
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.
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.
In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?
If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.
Write the sum of first n even natural numbers.
If m th term of an A.P. is n and nth term is m, then write its pth term.
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, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
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
If a, b, c are in A.P. and x, y, z are in G.P., then the value of xb − c yc − a za − b is
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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 ______.
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 ______.
