01 · THE FORMULA
Formula for the nth Term
Let a be the first term and d be the common difference of an AP. The n-th term (aₙ) is given by:
aₙ = a + (n - 1)dwhere a = first term, d = common difference, n = term number, aₙ = n-th term (or last term L).
nth Term from the End
If an AP has m terms, the n-th term from the end is equal to the (m - n + 1)th term from the beginning, or:
aₙ(end) = L - (n - 1)d (where L is the last term).
02 · SOLVED NCERT EXAMPLES
Step-by-Step Problem Solving
EXAMPLE 1
Find the 10th term of the AP: 2, 7, 12...
Given: a = 2, d = 7 - 2 = 5, n = 10.
Using aₙ = a + (n - 1)d:
a₁₀ = 2 + (10 - 1) × 5
a₁₀ = 2 + 9 × 5 = 2 + 45 = 47
a₁₀ = 2 + 9 × 5 = 2 + 45 = 47
EXAMPLE 2
Which term of the AP: 21, 18, 15... is -81?
Given: a = 21, d = 18 - 21 = -3, aₙ = -81.
aₙ = a + (n - 1)d
-81 = 21 + (n - 1)(-3)
-81 - 21 = -3(n - 1)
-102 = -3(n - 1) ⟹ n - 1 = 34 ⟹ n = 35
-81 = 21 + (n - 1)(-3)
-81 - 21 = -3(n - 1)
-102 = -3(n - 1) ⟹ n - 1 = 34 ⟹ n = 35
Hence, the 35th term of the AP is -81.
03 · QUICK SUMMARY
Key Takeaways
01
General term formula: aₙ = a + (n - 1)d.
02
If aₙ is given, solve for n to find the position of a term.
03
Term number n must always be a positive integer (1, 2, 3...).