Explanation

Series: 7, 9, 12, 17, 24, 35, ?

Step 1: Find differences

9 − 7 = 2

12 − 9 = 3

17 − 12 = 5

24 − 17 = 7

35 − 24 = 11

Differences: 2, 3, 5, 7, 11 → all prime numbers.

Step 2: Next prime after 11 = 13

Step 3: Add to last term

35 + 13 = 48

Explanation

Sequence: 6, 7, 11, 20, ?

Step 1: Find differences

7 − 6 = 1

11 − 7 = 4

20 − 11 = 9

The differences are 1, 4, 9 — which are 1², 2², 3².

Step 2: Next difference = 4² = 16

Step 3: Add to last term

20 + 16 = 36

Explanation

A circle can have only two parallel tangents — one on each opposite side.

These tangents are equidistant from the center of the circle.

Explanation

Multiples of 4 from 12 to 248 form an arithmetic series with difference 4.

Total number of such multiples = 60.

Explanation

Common difference = 7, and using AP formula gives aₙ = a₁ + (n−1)d.

Substituting values gives 21st term = 137.

Explanation

The pattern is a constant addition: 31 → 31 + 59 = 90.

Apply same rule: 43 + 59 = 102.

Explanation

The limit lim x→∞ 2/x is equal to 0.

As x approaches infinity, the denominator x becomes very large, and the numerator 2 remains constant.

Therefore, the ratio 2/x approaches 0.

Explanation

2 ×  2 = 4

4 ×  2 = 8

8 ×  2 = 16

16 ×  2 = 32

Explanation

Explanation