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
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Which term of the AP 21, 18, 15, …… is -81?
Find the middle term of the AP 6, 13, 20, …., 216.
Find the middle term of the AP 10, 7, 4, ……., (-62).
Find the 6th term form the end of the AP 17, 14, 11, ……, (-40).
The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
Find the sum of last ten terms of the AP: 8, 10, 12,.., 126.
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Find the sum of first 'n' even natural numbers.
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
Three numbers in A.P. have the sum of 30. What is its middle term?
