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in Arithmetic Progression by (44.3k points)
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एक समान्तर श्रेणी का 9 वाँ पद, दूसरे पद का 6 गुना है। यदि इसका 5 वाँ पद 22 है। तो समान्तर श्रेणी ज्ञात कीजिए।

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माना श्रेणी का प्रथम पद a तथा सार्वअन्तर d है। दिया है :

a9 = 6 × a2

⇒ a + 8d = 6(a + b)

⇒ a + 8d = 6a + 6d

⇒ 5a = 2d

⇒ a = 2d/5

तथा a5 = 22 …(1)

a + 4d = 22

समी० (1) से a का मान रखने पर,

2d/5 + 4d = 22

⇒ 2d + 20d = 22 × 5

⇒ 22d = 22 × 5

⇒ d = 5

अतः a = 2x5/5 = 2

अतः समान्तर श्रेणी 2, 7, 12, 17,…

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