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
Find the sum of odd integers from 1 to 2001.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
The pth, qth and rth terms of an A.P. are a, b, c respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0
Let < an > be a sequence. Write the first five term in the following:
a1 = 1 = a2, an = an − 1 + an − 2, n > 2
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
9, 7, 5, 3, ...
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.
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.
The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.
Find the sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.
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.
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
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.
We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?
Write the common difference of an A.P. whose nth term is xn + y.
Write the common difference of an A.P. the sum of whose first n terms is
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
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 ______.
Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.
If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.
