First term defines the starting value. Common difference is added repeatedly to generate subsequent terms. Sequence continues infinitely. Arithmetic pattern maintains constant difference between consecutive terms. Values grow steadily and evenly with equal steps. Each term can be found by adding common difference to previous term.
Arithmetic progression displays sequential numbers with constant difference between consecutive terms. First term establishes sequence beginning. Common difference stays fixed through progression. Each term can be calculated from previous term and common difference. Students learn finding nth term missing terms sequence patterns and sum of terms. Applications include real-world number patterns series analysis and problem-solving.
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Given:
pᵗʰ term = q. (1)
qᵗʰ term = p. (2)
Let a₁ be first term and d be common difference.
Using (1):
a₁ + (p-1)d = q. (3)
Using (2):
a₁ + (q-1)d = p. (4)
Subtracting (4) from (3):
(p-q)d = q-p
d = -1
Substituting d = -1 in (3):
a₁ + (p-1)(-1) = q
a₁ – p + 1 = q
a₁ = p + q – 1
Now, (p+q)ᵗʰ term = a₁ + (p+q-1)(-1)
= (p+q-1) + (p+q-1)(-1)
= p+q-1 – p-q+1
= 0
Therefore, (p+q)ᵗʰ term is 0 is the correct answer.