Advertisements
Advertisements
Question
Find t21, if S41 = 4510 in an A.P.
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
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?
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
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
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
How many two-digit number are divisible by 6?
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
Write an A.P. whose first term is a and common difference is d in the following.
Find the first term and common difference for the A.P.
5, 1, –3, –7,...
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
Find the sum (−5) + (−8)+ (−11) + ... + (−230) .
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first instalment of Rs. 1000. If he increases the instalment by Rs. 100 every month, what amount will be paid by him in the 30th instalment? What amount of loan does he still have to pay after the 30th instalment?
Find the sum of first 16 terms of the A.P. whose nth term is given by an = 5n – 3.
