Advertisements
Advertisements
प्रश्न
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
पर्याय
501th
502th
508th
none of these
Advertisements
उत्तर
In the given problem, let us take the first term as a and the common difference as d.
Here, we are given that,
`a_9 = 449` ...............(1)
`a_449 = 9 ` .................(2)
We need to find n
Also, we know,
`a_n = a + ( n- 1) d`
For the 9th term (n = 9),
`a_9 = a + ( 9 -1) d`
449 = a + 8d (Using 1 )
a = 449 - 8 d .................(3)
Similarly, for the 449th term (n = 449),
`a_449 = a + ( 449 - 1 )d`
9 = a + 448d (Using 2 )
a = 9 - 448 d .............(4)
Subtracting (3) from (4), we get,
a -a = ( 9 - 448d) - ( 449 - 8d)
0 = 9 - 448d - 449 + 8d
0 = -440 - 440d
440d = - 440
d = - 1
Now, to find a, we substitute the value of d in (3),
a = 449 - 8 (-1)
a = 449 + 8
a = 457
So, for the given A.P d = - 1 and a = 457
So, let us take the term equal to zero as the nth term. So,
`a_n = 457 + ( n- 1) ( -1 ) `
0 = 457 - n + 1
n = 458
So, n = 458
APPEARS IN
संबंधित प्रश्न
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all even integers between 101 and 999.
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
Which term of the AP 3,8, 13,18,…. Will be 55 more than its 20th term?
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Write an A.P. whose first term is a and common difference is d in the following.
The sequence −10, −6, −2, 2, ... is ______.
Find the sum (−5) + (−8)+ (−11) + ... + (−230) .
The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is ______.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
