Advertisements
Advertisements
Question
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
Advertisements
Solution
t18 = 52 and t39 = 148 S56 = ?
tn = a + (n-1)d
t18 = a +( 18 - 1) d
52 = a + 17 d ......(i)
t39 = a + (39 -1) d
∴ 148 = a + 38d ........(2)
Adding (1) and (2)
a + 17d = 52
a + 38d = 148
2a = 55d = 200 .......(3)
Sn = `n/2` [2a + (n - 1) d ]
S56 = `56/2` [2a + (56 -1) d]
= 28 [2a + 55d ]
= 28(200) [from eq (3)]
S56 = 5600
APPEARS IN
RELATED QUESTIONS
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by 30 days.
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of the following arithmetic progressions:
1, 3, 5, 7, ... to 12 terms
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are a – d, a, a + d).
The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is
Q.17
Find the sum of odd natural numbers from 1 to 101.
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment.
The sum of all two digit odd numbers is ______.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
