Advertisements
Advertisements
प्रश्न
How many three-digit numbers are divisible by 7?
उत्तर
Is a list of three-digit numbers divisible by 7.
105, 112, 119, …, 994
a = 105, d = 112 - 105 = 7, an = 994
∴ an = a + (n - 1)d
⇒ 994 = 105 + (n - 1) × 7
⇒ 994 = 105 + 7n - 7
⇒ 7n = 994 + 7 - 105
⇒ 7n = 1001 - 105
⇒ 7n = 896
⇒ n = `896/7`
⇒ n = 128
Hence, there are 128 three-digit numbers divisible by 7.
APPEARS IN
संबंधित प्रश्न
Find the number of terms in the following A.P.: 7, 13, 19, ..., 205.
Write the first five terms of the following sequences whose nth terms are:
an = (−1)n, 2n
Write the first five terms of the following sequences whose nth terms are:
an = n2 − n + 1
Which term of the A.P. 4, 9, 14, ... is 254?
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.
(i) 9, 15, 21, 27,…………
Find:
(ii) the 35th term of AP 20,17,14,11,..........
Find the nth term of the following Aps:
16, 9, 2, -5, …..
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3 (S20 − S10) ?
Which term of the AP: 27, 24, 21, ……… is zero?
37th term of the AP: `sqrtx, 3sqrtx, 5sqrtx, ....` is ______.
The (n - 1)th term of an A.P. is given by 7, 12, 17, 22,… is ______.
The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is ______.
The 10th term from the end of the A.P. 4, 9,14, …, 254 is ______.
Write the first three terms of the APs when a and d are as given below:
a = –5, d = –3
The 26th, 11th and the last term of an AP are 0, 3 and `- 1/5`, respectively. Find the common difference and the number of terms.
The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.
Which term of the AP: 53, 48, 43,... is the first negative term?
