Advertisements
Advertisements
Question
Find t21, if S41 = 4510 in an A.P.
Advertisements
Solution
For an A.P., let a be the first term and d be the common difference.
S41 = 4510 ......[Given]
Since Sn = `"n"/2 [2"a" + ("n" - 1)"d"]`,
S41 = `41/2 [2"a" + (41 - 1)"d"]`
∴ 4510 = `41/2 (2"a" + 40"d")`
∴ 4510 = `41/2 xx 2 ("a" + 20"d")`
∴ 4510 = 41(a + 20d)
∴ a + 20d = `4510/41`
∴ a + 20d = 110 .....(i)
Now, tn = a + (n – 1)d
∴ t21 = a + (21 – 1)d
= a + 20d
∴ t21 = 110 ......[From (i)]
APPEARS IN
RELATED QUESTIONS
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.
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Find the sum of first 15 multiples of 8.
Find the sum of all integers between 50 and 500, which are divisible by 7.
Find the sum of all 3-digit natural numbers, which are multiples of 11.
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
If the sum of first m terms of an AP is ( 2m2 + 3m) then what is its second term?
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If in an A.P. Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
Q.3
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Write the formula of the sum of first n terms for an A.P.
If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
