Advertisements
Advertisements
Question
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Advertisements
Solution
t11 = 16 and t21 = 29
t1 = ?, d = ? and t34 = ?
tn = a + (n - 1) d
t11 = a + (11 - 1) d
16 = a + 10 d ......(1)
t21 = a + (21 - 1) d
29 = a + 20d .........(2)
Subtracting equation (1) and (2)
a + 20 d = 29
a + 10 d = 16
_________________
10 d = 13
d = `13/10`
d = 1.3
Substituting d = 1.3 in equation (1)
16 = a + 10 d
a + 10 (1.3) = 16
a + 13 = 16
a = 16 - 13
a = 3
t34 = 3 + (34 - 1) (1.3)
= 3 + 33(1.3)
= 3 + 42.9
t34 = 45.9
APPEARS IN
RELATED QUESTIONS
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Which term of the A.P. 121, 117, 113 … is its first negative term?
[Hint: Find n for an < 0]
Find the sum 25 + 28 + 31 + ….. + 100
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
Find the 8th term from the end of the AP 7, 10, 13, ……, 184.
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
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) ?
The sequence −10, −6, −2, 2, ... is ______.
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
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.
Q.3
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
What is the sum of an odd numbers between 1 to 50?
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
The sum of first five multiples of 3 is ______.
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
Sum of 1 to n natural number is 45, then find the value of n.
