Explanation

For an A.P., nth term = a + (n-1)d, where a = first term, d = common difference

Given:  

a5 = a + 4d = 18  

a15 = a + 14d = 58  

Subtract: 10d = 40 → d = 4  

Put d=4 in a + 4d = 18 → a + 16 = 18 → a = 2

Sum of first n terms = n/2 [2a + (n-1)d]  

S25 = 25/2 [2×2 + 24×4]  

= 25/2 [4 + 96]  

= 25/2 × 100 = 25 × 50 = 1250

Last verified on 13-06-2026

Explanation

6-2=4, 12-6=6, 20-12=8, 30-20=10  

Differences go 4, 6, 8, 10... next is 12  

So 30 + 12 = 42

Last verified on 13-06-2026

Explanation

5 × 2 = 10

10 × 2 = 20

20 × 2 = 40

40 × 2 = 80

Last verified on 11-2026

Explanation

• 0 (single digit 0)
• 99 (two 9s)
• 888 (three 8s)

Explanation

Series: 1, 1, 2, 6, 24, 120, ?

This is factorial pattern:  

1 = 1!  

1 = 1!  

2 = 2!  

6 = 3!  

24 = 4!  

120 = 5!  

Next = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Last verified on 10-06-2026

Explanation

Sequence: 2, 5, 8, ...  

Check the pattern: 5 - 2 = 3, 8 - 5 = 3 → common difference d = 3. So it’s an A.P.

General term for A.P: aₙ = a₁ + (n-1)d  

Here a₁ = 2, d = 3  

aₙ = 2 + (n-1)3 = 2 + 3n - 3 = 3n - 1

Test: n=1 → 3(1)-1=2 ✓, n=2 → 5 ✓, n=3 → 8 ✓

Last verified on 07-06-2026

Explanation

In this series, each number is formed by adding the square of a natural number (1^2, 2^2, 3^2, .....) to the preceding number.

• 15 + 1² = 16
• 16 + 2² = 20
• 20 + 3² = 29 ← should be 29, but given 30
• 29 + 4² = 45
• 45 + 5² = 70

So the correct sequence should be:

15, 16, 20, 29, 45, 70

Therefore, 30 is the incorrect number

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Last updated by NS on 01 MAY 2026

Explanation

This is a geometric progression (GP) where each term is multiplied by 3:

1, 3, 9, 27, 81, 243, 729, 2187

Formula:

Here:

• a = 1
• r = 3
• n = 8

So:

8th term = 2187

Last updated by NA on 2 MAY 2026

Explanation

Explanation

Series:

6, 3, 12, 6, 24, ___

Step 1: Find a pattern

• 6 → 3 (÷2)
• 3 → 12 (×4)
• 12 → 6 (÷2)
• 6 → 24 (×4)

So the pattern alternates:
÷2, ×4, ÷2, ×4, ...

Step 2: Next term

$$24÷2=12$$

$$Last\; updated\; by\; NA\; on\; 25-April-2026$$