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
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20 − S10]
The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their mth terms
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
Is 184 a term of the AP 3, 7, 11, 15, ….?
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?
If the sum of first p terms of an AP is 2 (ap2 + bp), find its common difference.
If the common differences of an A.P. is 3, then a20 − a15 is
The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.
a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
`= 6 × square `
` =square`
The nth term of an A.P., the sum of whose n terms is Sn, is
Q.6
Q.16
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
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?
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :
Activity:
Given A.P. : 7, 13, 19, 25, ..........
Here first term a = 7; t19 = ?
tn + a + `(square)`d .........(formula)
∴ t19 = 7 + (19 – 1) `square`
∴ t19 = 7 + `square`
∴ t19 = `square`
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
