Advertisements
Advertisements
प्रश्न
In an AP given a = 3, n = 8, Sn = 192, find d.
Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.
d, if a = 3, n = 8 and Sn = 192
Advertisements
उत्तर १
Given that, a = 3, n = 8, Sn = 192
`S_n = n/2 [2a+(n-1)d]`
`192 = 8/2[2xx3+(8-1)d]`
192 = 4 [6 + 7d]
48 = 6 + 7d
42 = 7d
`d = 42/7`
d = 6
उत्तर २
Here, we have an A.P. whose first term (a), the sum of first n terms (Sn) and the number of terms (n) are given. We need to find the common difference (d).
Here,
First term (a) = 3
Sum of n terms (Sn) = 192
Number of terms (n) = 8
So here we will find the value of n using the formula, an = a + (a - 1)d
So, to find the common difference of this A.P., we use the following formula for the sum of n terms of an A.P
`S_n = n/2 [2a + (n -1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
So, using the formula for n = 8, we get,
`S_8 = 8/2 [2(3) + (8 - 1)(d)]`
192 = 4[6 + (7) (d)]
192 = 24 + 28d
28d = 192 - 24
Further solving for d
`d = 168/28`
d = 6
Therefore, the common difference of the given A.P. is d = 6.
APPEARS IN
संबंधित प्रश्न
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
In an AP given an = 4, d = 2, Sn = −14, find n and a.
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
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
If the sum of first m terms of an AP is ( 2m2 + 3m) then what is its second term?
Choose the correct alternative answer for the following question .
What is the sum of the first 30 natural numbers ?
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`
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
Write the sum of first n odd natural numbers.
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to
The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
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 famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
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.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
The sum of 40 terms of the A.P. 7 + 10 + 13 + 16 + .......... is ______.
