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
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Find the sum of all integers between 84 and 719, which are multiples of 5.
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
If the numbers (2n – 1), (3n+2) and (6n -1) are in AP, find the value of n and the numbers
How many terms of the AP `20, 19 1/3 , 18 2/3, ...` must be taken so that their sum is 300? Explain the double answer.
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
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.
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
Q.18
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)
Three numbers in A.P. have the sum of 30. What is its middle term?
