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
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
In a flower bed, there are 43 rose plants in the first row, 41 in second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?
Write an A.P. whose first term is a and common difference is d in the following.
a = 6, d = –3
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P.
The first term of an A.P. is p and its common difference is q. Find its 10th term.
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
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
If a = 6 and d = 10, then find S10
If ₹ 3900 will have to be repaid in 12 monthly instalments such that each instalment being more than the preceding one by ₹ 10, then find the amount of the first and last instalment
The sum of first n terms of the series a, 3a, 5a, …….. is ______.
Find the sum of first seven numbers which are multiples of 2 as well as of 9.
Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)
The sum of all two digit numbers is ______.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is ______.
