Advertisements
Advertisements
प्रश्न
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
Advertisements
उत्तर
Let a be the first term and d be the common difference of the AP. Then,
`10 xx a_10 = 15 xx a_15 ` (Given)
⇒10(a +9d) = 15 (a+14d) { an = a+ (n-1)d]
⇒ 2 (a + 9d)=(a +14d)
⇒ 2a + 18d = 3a + 42d
⇒ a= -24d
⇒a + 24d = 0
⇒ a+ (25-1) d=0
⇒ a25 =0
Hence, the 25th term of the AP is 0.
APPEARS IN
संबंधित प्रश्न
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
Find how many integers between 200 and 500 are divisible by 8.
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
The first and last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term form the end is ( a + l ).
How many two-digit number are divisible by 6?
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
Q.20
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.
Find the sum of first seven numbers which are multiples of 2 as well as of 9.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
