Question
Download Solution PDFThe sum of (p + q)th and (p – q)th terms of an AP is equal to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The nth term of an AP is given by: Tn = a + (n - 1) × d, where a = first term and d = common difference.
Calculation:
As we know that, the nth term of an AP is given by: Tn = a + (n - 1) × d, where a = first term and d = common difference.
Let a be the first term and d is the common difference.
\(\Rightarrow \;{a_{p + q}} = a + \left( {p + q - 1} \right) \times d\) ...1)
\(\Rightarrow \;{a_{p - q}} = a + \left( {p - q - 1} \right) \times d\) ...2)
By adding (1) and (2), we get
\(\Rightarrow \;{a_{p + q}} + {a_{p - q}} = 2\;a + 2\;\left( {p - 1} \right)d = 2 \times \left[ {a + \left( {p - 1} \right)d} \right] = 2 \times {a_p}\)Last updated on May 30, 2025
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