Advertisements
Advertisements
प्रश्न
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Advertisements
उत्तर
The given sequence is 20, 19`1/4`,18`1/2`,17`3/4`,...
First term, a = 20
Common difference, d = `19 1/4 - 20 = (77 - 80)/4 = -3/4`
Let the nth term of the AP be the first negative term
So `a_n < 0`
`=> a + (n - 1)d < 0`
`=>20 + (n - 1)(-3/4) < 0`
`=> 83/4 - (3n)/4 < 0`
`=> 83 - 3n < 0`
`=> 3n > 83`
`=> n > 27 2/3`
`=> n >= 28`
Thus, the 28th term is the first negative term of the given AP
APPEARS IN
संबंधित प्रश्न
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.
If the term of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero
In an AP given a3 = 15, S10 = 125, find d and a10.
How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
Find the middle term of the AP 10, 7, 4, ……., (-62).
The sum of first n odd natural numbers is ______.
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
