Advertisements
Advertisements
प्रश्न
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
Advertisements
उत्तर
Since, the total number of terms (n) = 11 ...[odd]
∴ Middle most term = `(n + 1)^("th")/2` term
= `((11 + 1)/2)^("th")` term
= 6th term
Given that,
a6 = 30 ...[∵ an = a + (n − 1)d]
⇒ a + (6 − 1)d = 30
⇒ a + 5d = 30 ...(i)
∵ Sum of n terms of an AP,
Sn = `n/2[2a + (n - 1)d]`
∴ S11 = `11/2[2a + (11 - 1)d]`
= `11/2(2a + 10d)`
= 11(a + 5d)
= 11 × 30 ...[From equation (i)]
= 330
संबंधित प्रश्न
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
In an AP given l = 28, S = 144, and there are total 9 terms. Find a.
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
Find the sum of the following arithmetic progressions:
−26, −24, −22, …. to 36 terms
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
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 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Find the three numbers in AP whose sum is 15 and product is 80.
If k,(2k - 1) and (2k - 1) are the three successive terms of an AP, find the value of k.
If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
Write the sum of first n even natural numbers.
If 18, a, b, −3 are in A.P., the a + b =
If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
The sum of all two digit odd numbers is ______.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
