How many three-digit natural numbers are divisible by 7?

Question

✓

Answer

The three-digit natural numbers divisible by 7 are 105, 112, 119, ..., 994.
Clearly, three number are in AP.
Here, a = 105 and d = 112 - 105 = 7
Let this AP contains n terms. Then,
$a_n = 994$
$\Rightarrow 105 + (n - 1) \times 7 = 994$
$\Rightarrow 7n + 98 = 994 [a_n = a + (n - 1)d]$
$\Rightarrow 7n = 994 - 98 = 896$
$\Rightarrow n = 128$
Hence, there are 128 three-digit numbers divisible by 7.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Arithmetic Progressions→Arithmetic Progressions — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Solve the following system of linear equation graphically and shade the region between the two lines and x-axis:

3x + 2y -11 = 0,

2x - 3y + 10 = 0.

→

Two dice, one blue and one grey, are thrown at the same time.Complete the following table:
Event: Sum on 2 dice 2 3 4 5 6 7 8 9 10 11 12
Probability $\frac{1}{{36}}$ $\frac{5}{{36}}$ $\frac{1}{{36}}$
A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument? Justify your answer.