Advertisements
Advertisements
प्रश्न
Find the sum of first 24 terms of the A.P. a1, a2, a3, ... if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.
उत्तर
We know that in an A.P., the sum of the terms equidistant from the beginning and end is always the same and is equal to the sum of first and last term.
Therefore d = b – a
i.e., a1 + a24 = a5 + a20
= a10 + a15
It is given that (a1 + a24) + (a5 + a20) + (a10 + a15) = 225
⇒ (a1 + a24) + (a1 + a24) + (a1 + a24) =225
⇒ 3(a1 + a24) = 225
⇒ a1 + a24 = 75
We know that Sn = `n/2[a + 1]`
Where a is the first term and l is the last term of an A.P.
Thus, S24 = `24/2 [a_1 + a_24]`
= 12 × 75
= 900
APPEARS IN
संबंधित प्रश्न
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Let < an > be a sequence defined by a1 = 3 and, an = 3an − 1 + 2, for all n > 1
Find the first four terms of the sequence.
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Find:
nth term of the A.P. 13, 8, 3, −2, ...
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of first n odd natural numbers.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
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.
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
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 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 odd natural numbers.
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [cosec a1cosec a2 + cosec a1 cosec a3 + .... + cosec an − 1 cosec an] is
In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is
If in an A.P., Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
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 for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.
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
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
