Advertisements
Advertisements
प्रश्न
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
Advertisements
उत्तर
Given, a4 + a8 = 24
a6 + a10 = 44
Let the first term of A.P be a and common difference be d
a4 + a8 = 24
a + 3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12 ...(1)
a6 + a10 = 44
a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22 ...(2)
From equation (1) and (2)
d = 5 and a = – 13
∴ First term of A.P. = – 13
and Common difference = 5
Sn = `n/2[2a + (n - 1)d]`
S25 = `25/2[-26 + 24 xx 5]`
= `25/2 xx 94`
Sum of 25 terms = 25 × 47 = 1175
APPEARS IN
संबंधित प्रश्न
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
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
The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
Sum of 1 to n natural numbers is 36, then find the value of n.
If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
x is nth term of the given A.P. an = x find x .
An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
- amount of installments paid in the 9th month.
- total amount paid in the installment scheme.
Q.16
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
