Advertisements
Advertisements
Question
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
Advertisements
Solution
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
RELATED QUESTIONS
The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their mth terms
Find the sum of the odd numbers between 0 and 50.
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
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 all integers between 50 and 500, which are divisible by 7.
Find the sum of all even integers between 101 and 999.
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
Simplify `sqrt(50)`
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
x is nth term of the given A.P. an = x find x .
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
Find the sum of odd natural numbers from 1 to 101
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
