Advertisements
Advertisements
प्रश्न
In an AP, if Sn = n(4n + 1), find the AP.
Advertisements
उत्तर
We know that, the nth term of an AP is
an = Sn – Sn – 1
an = n(4n + 1) – (n – 1){4(n – 1) + 1} ...[∵ Sn = n(4n + 1)]
⇒ an = 4n2 + n – (n – 1)(4n – 3)
= 4n2 + n – 4n2 + 3n + 4n – 3
= 8n – 3
Put n = 1,
a1 = 8(1) – 3
= 5
Put n = 2,
a2 = 8(2) – 3
= 16 – 3
= 13
Put n = 3,
a3 = 8(3) – 3
= 24 – 3
= 21
Hence, the required AP is 5, 13, 21,...
APPEARS IN
संबंधित प्रश्न
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.
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
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 the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
The first and last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term form the end is ( a + l ).
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
Find the sum of all multiples of 9 lying between 300 and 700.
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
Write the sum of first n odd natural numbers.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
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
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.
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
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
