Advertisements
Advertisements
प्रश्न
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
Advertisements
उत्तर
The given AP is 27, 24, 21, ..
First term of the AP = 27
Common difference = 24 − 27 = −3
Let the sum of the first x terms of the AP be 0.
Sum of first x terms = `x/2`[2×27+(x−1)(−3)]=0
⇒`x/2`[54+(−3x+3)]=0
⇒x(54−3x+3)=0
⇒x(57−3x)=0
Now, either x = 0 or 57 − 3x = 0.
Since the number of terms cannot be 0, x≠0.
∴ 57 − 3x = 0
⇒ 57 = 3x
⇒ x = 19
Thus, the sum of the first 19 terms of the AP is 0.
APPEARS IN
संबंधित प्रश्न
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is
Find the sum of numbers between 1 to 140, divisible by 4
Three numbers in A.P. have the sum of 30. What is its middle term?
