Advertisements
Advertisements
Question
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
Advertisements
Solution
Given equation is,
– 4 + (–1) + 2 + 5 + … + x = 437
Here, –4 – 1 + 2 + 5 + … + x is in A.P.
Then, a = -4, d = -1 + 4 = 3, l = x
Given: Sn = 437
⇒ `"n"/2[2"a" + ("n" - 1)"d"]=437`
⇒ n[-8 + 3n - 3] = 874
⇒ 3n2 - 11n - 874 = 0
⇒ 3n2 - 57n + 46n - 874 = 0
⇒ 3n(n - 19) + 46(n -19) = 0
⇒ (n - 19) (3n + 46) = 0
⇒ n - 19 = 0, n = 19
⇒ 3n + 46 = 0
n = `-46/3` (Impossible)
Hence, n = 19
So, l = a + (n - 1)d
x = -4 + (19 - 1) 3
= -4 + 18 × 3
= -4 + 54
x = 50
APPEARS IN
RELATED QUESTIONS
Find the sum of all 3-digit natural numbers, which are multiples of 11.
Find the sum of all multiples of 7 lying between 300 and 700.
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Find the sum of the following Aps:
9, 7, 5, 3 … to 14 terms
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
Find the sum (−5) + (−8)+ (−11) + ... + (−230) .
The sum of first n odd natural numbers is ______.
If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 – S4)
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
