Advertisements
Advertisements
प्रश्न
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
Advertisements
उत्तर
In an A.P., 17th term is 7 more than its 10th term. ...(Given)
The formula for nth term of an A.P. is tn = a + (n − 1)d
The 10th term can be written as,
t10 = a + (10 − 1)d
t10 = a + 9d
The 17th term can be written as,
t17 = a + (17 − 1)d
t17 = a + 16d
Now, according to the question,
t17 = 7 + t10
Substituting the value of t17 and t10 in the above equation,
∴ a + 16d = 7 + a + 9d
∴ 16d = 7 + 9d
∴ 16d − 9d = 7
∴ 7d = 7
∴ d = `7/7` = 1
Hence, the common difference of the given AP is 1.
संबंधित प्रश्न
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 the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
How many multiples of 4 lie between 10 and 250?
Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her week, her weekly savings become Rs 20.75, find n.
Find the sum of the following APs:
2, 7, 12, ..., to 10 terms.
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
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.]
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
Find the sum of first 12 natural numbers each of which is a multiple of 7.
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
If the sum of first n terms is (3n2 + 5n), find its common difference.
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
What is the sum of first 10 terms of the A. P. 15,10,5,........?
Q.5
Find the sum of all members from 50 to 250 which divisible by 6 and find t13.
The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is `(1)/(3)`. Calculate the first and the thirteenth term.
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
