Advertisements
Advertisements
प्रश्न
In an AP given d = 5, S9 = 75, find a and a9.
Advertisements
उत्तर
Here, d = 5 and S9 = 75 (given)
∵ Sn = `"n"/2` [a + an]
⇒ `S_9 = 9/2[a + a_9] = 75`
⇒ 3a + 3a9 = 50 ...(1)
∵ `S_n = n/2[2a + (n - 1) xx d]`
⇒ `S_9 = 9/2[2a + (9 - 1) xx 5] = 75`
⇒ `9/2[2a + 40] = 75`
⇒ 9a + 180 = 75
⇒ 9a = 75 - 180
⇒ 9a = -105
⇒ a = `-105/9`
⇒ a = `-35/3` ...(2)
By substituting the value of a from equation (2) in equation (1),
`3 xx (-35/3) + 3a_9 = 50`
⇒ -35 + 3a9 = 50
⇒ 3a9 = 50 + 35
⇒ 3a9 = 85
⇒ a9 = `85/3`
APPEARS IN
संबंधित प्रश्न
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed, and how many logs are in the top row?
Find the sum of first 8 multiples of 3
Find the sum of all integers between 50 and 500, which are divisible by 7.
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero
How many three-digit numbers are divisible by 9?
Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.
Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
If the seventh term of an A.P. is \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.
The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
The sum of first 20 odd natural numbers is
If the nth term of an AP is (2n +1), then the sum of its first three terms is ______.
Find the sum of the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
