Explanation

an = 5n − 7

This is an arithmetic sequence with first term a = -2 and common difference d = 5.

General formula: an = a + (n−1)d = -2 + (n−1)×5 = 5n − 7.

Explanation

Given Four digits are 0,3,5,8

To write the smallest 4-digit numbers using the above digits, we must arrange them in ascending order.

Here, we get

0358 = 358 [It has only 3 digits ]

3058

Therefore,

The smallest 4-digit number using

0,3,5,8 is 3058.

Explanation

Looking at the pattern:

20 → 20 (no change)

20 → 19 (decrease by 1)

19 → 16 (decrease by 3)

16 → 17 (increase by 1)

17 → 13 (decrease by 4)

13 → 14 (increase by 1)

14 → 11 (decrease by 3)

Now, we continue the alternating pattern:

11 → 12 (increase by 1)

12 → 9 (decrease by 3)

The next two numbers are 10, 10.

Explanation

First and Third Numbers:

9² = 81

8² = 64

So for 10: 10² = 100 → third number is 100

Now the middle number:

9 × 5 = 45

8 × 4.5 = 36

Seems like:

Middle number = First number × 5 (for 9), and × 4.5 (for 8)

Let’s check the pattern:

9 → ×5 = 45

8 → ×4.5 = 36

So 10 → ×4 = 40

Final Set:

10 (40) (100)

Explanation

Now, let's examine the differences between consecutive terms:

17 − 6 = 11

39 − 17 = 22

72 − 39 = 33

The pattern of differences: +11, +22, +33 → increasing by 11 each time.

Next difference should be: +44

So,

72 + 44 = 116

Explanation: Differences follow a pattern: +11, +22, +33, +44.