Advertisements
Advertisements
प्रश्न
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference
Advertisements
उत्तर
Let a be the first term and d be the common difference of the AP. Then,
a4 = 11
⇒ a+ (4-1) d = 11 [ an = a + (n-1) d]
⇒ a+3d = 11 ..............(1)
Now
a5 + a7 = 34 ( Given)
⇒ (a 4d) +(a + 6d ) = 34
⇒ 2a + 10d = 34
⇒ a+ 5d = 17 ...........(2)
From (1) and (2), we get
11-3d + 5d = 17
⇒ 2d = 17 - 11 = 6
⇒ d = 3
Hence, the common difference of the AP is 3.
APPEARS IN
संबंधित प्रश्न
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
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 ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
How many multiples of 4 lie between 10 and 250?
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
In an AP Given a12 = 37, d = 3, find a and S12.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, .... as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)
[Hint: Length of successive semicircles is l1, l2, l3, l4, ... with centres at A, B, A, B, ... respectively.]
In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.
Which term of AP 72,68,64,60,… is 0?
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
Q.6
Q.15
Find the sum of the first 10 multiples of 6.
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Find the sum of all odd numbers between 351 and 373.
Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?
Hence find the sum of all the terms of the Arithmetic Progression (A.P.)
The sum of 41 terms of an A.P. with middle term 40 is ______.
