DP AWO/TPO21 Jan 2026Shift 2Progression (AP & GP)

If the 18th term of an A.P. is zero, then seven times the seventh term is ____ times the eleventh term.

अगर किसी समांतर (Parallel) श्रेणी (Series) का 18वाँ पद शून्य है, तो सातवें पद का सात गुना ग्यारहवें पद का ____ गुना है।

Answer और ExplanationAnswer and explanation

Answer: (D) 11

दिया है: T18 = 0
⇒ a + 17d = 0 ⇒ a = −17d
T7 = a + 6d = −17d + 6d = −11d
T11 = a + 10d = −17d + 10d = −7d
7 × T7 = 7 × (−11d) = −77d = 11 × (−7d) = 11 × T11
✓
सातवें पद का सात गुना, ग्यारहवें पद का 11 गुना है।
Given: T18 = 0
⇒ a + 17d = 0 ⇒ a = −17d
T7 = a + 6d = −17d + 6d = −11d
T11 = a + 10d = −17d + 10d = −7d
7 × T7 = 7 × (−11d) = −77d = 11 × (−7d) = 11 × T11
✓
Seven times the seventh term is 11 times the eleventh term.
SMART APPROACH

d = 1 रख दें। तब a = −17, T7 = −11, T11 = −7। 7 × (−11) = −77 = 11 × (−7)। उत्तर 11। ऐसे प्रश्नों में हर पद (Term) को "शून्य वाले पद से कितनी दूर है" से सोचें: T7, T18 से 11 जगह पहले है, तो T7 = −11d; T11, 7 जगह पहले है, तो T11 = −7d।

Put d = 1. Then a = −17, T7 = −11, T11 = −7. 7 × (−11) = −77 = 11 × (−7). Answer 11. In general, in such questions think of each term as "how far it is from the zero term": T7 is 11 places before T18, so T7 = −11d; T11 is 7 places before it, so T11 = −7d.

Source: DP AWO/TPO · 21 Jan 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: DP AWO/TPO · 21 Jan 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.