Advertisements
Advertisements
प्रश्न
How many consecutive odd integers beginning with 5 will sum to 480?
उत्तर
5, 7, 9, 11, 13,…
Sn = 480
a = 5, d = 2, Sn = 480
Sn = `"n"/2 (2"a" + ("n" - 1)"d")`
480 = `"n"/2 [2 xx 5 + ("n" - 1)2]`
= `"n"/2[10 + 2"n" - 2]`
480 = `"n"/2[8 + 2"n"]`
8n + 2n2 = 960
2n2 + 8n – 960 = 0
⇒ n2 + 4n – 480 = 0
⇒ n2 + 24n – 20n – 480 = 0
⇒ n(n + 24) – 20(n + 24) = 0
⇒ (n – 20)(n + 24) = 0
⇒ n = 20, – 24
No. of terms cannot be negative.
∴ No. of consecutive odd integers beginning with 5 will sum to 480 is 20.
APPEARS IN
संबंधित प्रश्न
The sum of first n terms of a certain series is given as 2n2 – 3n. Show that the series is an A.P.
Find the sum of all odd positive integers less than 450
Find the sum of all natural numbers between 602 and 902 which are not divisible by 4.
Raghu wish to buy a laptop. He can buy it by paying ₹ 40,000 cash or by giving it in 10 installments as ₹ 4800 in the first month, ₹ 4750 in the second month, ₹ 4700 in the third month and so on. If he pays the money in this fashion, find total amount paid in 10 installments
A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two bricks less than the previous step
How many bricks are required for the top most step?
A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two bricks less than the previous step
How many bricks are required to build the stair case?
If S1, S2 , S3, …., Sm are the sums of n terms of m A.P.'s whose first terms are 1, 2, 3, ……, m and whose common differences are 1, 3, 5, …., (2m – 1) respectively, then show that S1 + S2 + S3 + ... + Sm = `1/2` mn(mn + 1)
An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is
In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?
If A = 265 and B = 264 + 263 + 262 …. + 20 identify of the following is true?
