Advertisements
Advertisements
प्रश्न
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
For what value of n, the nth term of A.P. 63, 65, 67, …….. and nth term of A.P. 3, 10, 17, …….. are equal to each other?
उत्तर
Consider the A.P. 63, 65, 67, …
a = 63
d = a2 − a1 = 65 − 63 = 2
nth term of this A.P. = an = a + (n − 1)d
an = 63 + (n − 1)2
an = 63 + 2n − 2
an = 61 + 2n ...(1)
3, 10, 17, …
a = 3
d = a2 − a1
= 10 − 3
= 7
nth term of this A.P. = 3 + (n − 1) 7
an = 3 + 7n − 7
an = 7n − 4 ...(2)
It is given that, nth term of these A.P.s are equal to each other.
Equating both these equations, we obtain
61 + 2n = 7n − 4
61 + 4 = 5n
5n = 65
n = 13
Therefore, 13th terms of both these A.P.s are equal to each other.
APPEARS IN
संबंधित प्रश्न
If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
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
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
In an AP given a3 = 15, S10 = 125, find d and a10.
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.
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
How many two-digit number are divisible by 6?
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.
Find the sum of all 2 - digit natural numbers divisible by 4.
Find the sum: 1 + 3 + 5 + 7 + ... + 199 .
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 the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
Q.2
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Solve for x : 1 + 4 + 7 + 10 + … + x = 287.
Show that a1, a2, a3, … form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
The first term of an AP of consecutive integers is p2 + 1. The sum of 2p + 1 terms of this AP is ______.
In an AP, if Sn = n(4n + 1), find the AP.
If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 – S4)
Sum of 1 to n natural number is 45, then find the value of n.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
