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
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?
[Hint: number of rungs = `250/25+ 1`]
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
Write an A.P. whose first term is a and common difference is d in the following.
The Sum of first five multiples of 3 is ______.
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
- amount of installments paid in the 9th month.
- total amount paid in the installment scheme.
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20,......
Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]`
S100 = `square/2 [24 + (100 - 1)"d"]`
= `50(24 + square)`
= `square`
= `square`
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment.
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
