Advertisements
Advertisements
प्रश्न
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
Advertisements
उत्तर
Let Sn denotes the sum of first n terms of the AP.
∴ sn = 3n2 + 6n
⇒ `s_(n-1 )= 3 (n-1)^2 + 6 (n-1)`
= 3 ( n2 - 2n + 1) + 6 (n-1)
= 3n2 - 3
∴ nth term of the AP , an
= sn = sn-1
= (3n2 + 6n) - ( 3n2 -3)
= 6n + 3
Putting n=15,we get
a15 = 6 × 15 + 3 = 90 + 3 = 93
Hence, the nth term is (6n + 3) and 15th term is 93.
APPEARS IN
संबंधित प्रश्न
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
Find the sum of the following arithmetic progressions:
−26, −24, −22, …. to 36 terms
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
Which term of the AP 21, 18, 15, … is zero?
Write an A.P. whose first term is a and common difference is d in the following.
If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is
Q.20
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
What is the sum of an odd numbers between 1 to 50?
The sum of first ten natural number is ______.
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
