Advertisements
Advertisements
Question
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Solution
Given that,
a = 17
l = 350
d = 9
Let there be n terms in the A.P.
l = a + (n − 1) d
350 = 17 + (n − 1)9
9n = 350 + 9 - 17
9n = 359 - 17
9n = 342
⇒ n = `342/9`
⇒ n = 38
Sn = `n/2(a+l)`
Sn = `38/2(17+350)`
= 19 × 367
= 6973
Thus, this A.P. contains 38 terms and the sum of the terms of this A.P. is 6973.
APPEARS IN
RELATED QUESTIONS
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
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 22 terms of the A.P. : 8, 3, –2, ………
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
Find the 8th term from the end of the AP 7, 10, 13, ……, 184.
How many three-digit numbers are divisible by 9?
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
The common difference of an A.P., the sum of whose n terms is Sn, is
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
Q.10
Q.19
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
In an A.P. a = 2 and d = 3, then find S12
If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.
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]
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
Find the sum of first 16 terms of the A.P. whose nth term is given by an = 5n – 3.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
