Advertisements
Advertisements
प्रश्न
If (2p +1), 13, (5p -3) are in AP, find the value of p.
Advertisements
उत्तर
Let (2p +1),13,(5p -3) be three consecutive terms of an AP.
Then 13-(2p +1) = (5p -3 )-13
⇒ 7p = 28
⇒ p= 4
∴ When p = 4,(2p +1) ,13 and (5p- 3) from three consecutive terms of an AP .
APPEARS IN
संबंधित प्रश्न
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
The sum of n terms of three arithmetical progression are S1 , S2 and S3 . The first term of each is unity and the common differences are 1, 2 and 3 respectively. Prove that S1 + S3 = 2S2
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
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 sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of all 3 - digit natural numbers which are divisible by 13.
Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
If the sum of first p term of an A.P. is ap2 + bp, find its common difference.
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
In an A.P. a = 2 and d = 3, then find S12.
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
