Essential NIFT GAT 2026 Arithmetic Progression Questions

When you're sitting for NIFT GAT 2026, the math section can either boost your score or pull it down, and AP questions are something you'll definitely encounter. As far as arithmetic progression is concerned, it is not difficult once you learn the formulas and their applications. The ordinary person usually gets messed up with the formulas, not because they did not understand the concept, but because they rushed through the calculations or forgot which formula applies to which case. Prior practice of all kinds of questions will surely give you an edge: you will immediately notice the patterns and solve them faster on the day of the examination.

Essential NIFT GAT 2026 Arithmetic Progression Questions with Step-by-Step Solutions

Check here some of the important arithmetic progression question types you will encounter in the NIFT GAT 2026:

Question 1: Finding the nth Term

Problem: The 5th term of an AP is 23 and the 12th term is 58. Find the 20th term of this sequence.

Solution:

We know that the nth term formula is: an = a + (n-1)d

For the 5th term: a + 4d = 23 ... (equation 1)

For the 12th term: a + 11d = 58 ... (equation 2)

Subtracting equation 1 from equation 2:

• (a + 11d) - (a + 4d) = 58 - 23
• 7d = 35
• d = 5

Now substituting d = 5 in equation 1:

• a + 4(5) = 23
• a + 20 = 23
• a = 3

For the 20th term:

• a20 = a + 19d
• a20 = 3 + 19(5)
• a20 = 3 + 95
• a20 = 98

Question 2: Sum of n Terms

Problem: Find the sum of the first 25 terms of an arithmetic progression whose first term is 7 and common difference is 3.

Solution:

The sum of n terms formula is: Sn = n/2 [2a + (n-1)d]

Substituting the values:

• S25 = 25/2 [2(7) + (25-1)(3)]
• S25 = 25/2 [14 + 24(3)]
• S25 = 25/2 [14 + 72]
• S25 = 25/2 × 86
• S25 = 25 × 43
• S25 = 1075

Question 3: Finding the Number of Terms

Problem: How many terms of the AP 18, 16, 14, 12... must be taken so that their sum is 60?

Solution:

Using the sum formula: Sn = n/2 [2a + (n-1)d]

Substituting:

• 60 = n/2 [2(18) + (n-1)(-2)]
• 60 = n/2 [36 - 2n + 2]
• 60 = n/2 [38 - 2n]
• 120 = n(38 - 2n)
• 120 = 38n - 2n^2
• 2n^2 - 38n + 120 = 0
• n^2 - 19n + 60 = 0

Factorizing:

• (n - 15)(n - 4) = 0
• n = 15 or n = 4

Both are mathematically correct, but checking:

• For n = 4: S4 = 60 ✓
• For n = 15: S15 = 60 ✓

Answer: Either 4 terms or 15 terms (This happens because after 4 terms, the sum reaches 60, then decreases as negative terms are added, and reaches 60 again at 15 terms)

Question 4: Three Numbers in AP

Problem: Three numbers are in AP. Their sum is 27 and their product is 648. Find the three numbers.

Solution:

Let the three numbers in AP be: (a-d), a, (a+d)

Sum: (a-d) + a + (a+d) = 27

• 3a = 27
• a = 9

Product: (a-d) × a × (a+d) = 648

• (9-d) × 9 × (9+d) = 648
• 9(9-d)(9+d) = 648
• (9-d)(9+d) = 72
• 81 - d^2 = 72
• d^2 = 9
• d = ±3

If d = 3: Numbers are 6, 9, 12 If d = -3: Numbers are 12, 9, 6

Answer: The three numbers are 6, 9, and 12

Question 5: Finding Common Difference from Sum

Problem: The sum of first 10 terms of an AP is 155 and the sum of first 20 terms is 610. Find the common difference.

Solution:

Using: Sn = n/2 [2a + (n-1)d]

For n = 10:

• 155 = 10/2 [2a + 9d]
• 155 = 5[2a + 9d]
• 31 = 2a + 9d ... (equation 1)

For n = 20:

• 610 = 20/2 [2a + 19d]
• 610 = 10[2a + 19d]
• 61 = 2a + 19d ... (equation 2)

Subtracting equation 1 from equation 2:

• (2a + 19d) - (2a + 9d) = 61 - 31
• 10d = 30
• d = 3

Question 6: Middle Term of an AP

Problem: If the first term of an AP is 8 and the last term is 56, and there are 13 terms in total, find the middle term.

Solution:

First, let's find the common difference using: l = a + (n-1)d

• 56 = 8 + (13-1)d
• 56 = 8 + 12d
• 48 = 12d
• d = 4

For an AP with odd number of terms, middle term is at position (n+1)/2 = (13+1)/2 = 7th position

7th term:

• a7 = a + 6d
• a7 = 8 + 6(4)
• a7 = 8 + 24
• a7 = 32

Alternatively, middle term = (first term + last term)/2 = (8 + 56)/2 = 32

These six question types will help you build a solid base for addressing any AP problem during NIFT GAT 2026. The actual trick lies in knowing the two main formulas by heart and then being careful with substitutions in calculations. Keep practicing these patterns, keep calm in the exam, and you will be walking free through any arithmetic progression questions.

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