Advertisements
Advertisements
प्रश्न
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
Advertisements
उत्तर
In the given AP, let the first be a and the common difference be d.
Then, tn = a + (n-1)d
Now , T4 = a + (4-1) d
⇒ a +3d = 0 ....................(1)
⇒ a = -3d
Again T11 = a + (11-1) d = a + 10 d
= -3d + 10d = 7d [ Using (1)]
Also , T25 = a + ( 25-1) d = a + 24d = - 3d + 24 d = 21d [Using (1)]
i.e . , T25 = 3 × 7d = ( 3 × T 11)
Hence, 25th term is triple its 11th term.
APPEARS IN
संबंधित प्रश्न
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3
Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
Find the sum of all even integers between 101 and 999.
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
Find the 8th term from the end of the AP 7, 10, 13, ……, 184.
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) ?
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
The sum of first ten natural number is ______.
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
Three numbers in A.P. have the sum of 30. What is its middle term?
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
