Advertisements
Advertisements
प्रश्न
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of first n odd natural numbers
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :
Activity:
Given A.P. : 7, 13, 19, 25, ..........
Here first term a = 7; t19 = ?
tn + a + `(square)`d .........(formula)
∴ t19 = 7 + (19 – 1) `square`
∴ t19 = 7 + `square`
∴ t19 = `square`
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
