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12. क्या समांतर श्रेढ़ी \( 18,15 \frac{1}{2}, 13, \ldots \ldots . . \) का एक पद \( -47 \) है? यदि हाँ तो कौनसा पद है? |
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Answer» \(18, 15\frac12, 13, ....\) \(\because a= a_1 = 18\) & \(d = a_2 - a_1 = 15\frac 12 - 18 = \frac{31}2 - 18 = \frac{31 - 36}2 = \frac{-5}2\) or \(d = a_3 - a_2 = 13 - 15 \frac 12 = 13 - \frac{31}2 = \frac {26 - 31} 2 = \frac {-5}2\) Let \(a_n = -47\) \(\therefore a + (n - 1)d = -47\) ⇒ \(18 + (n -1)(\frac{-5}2) = -47\) ⇒ \(-\frac 52 (n - 1) = - 47 - 18 = -65\) ⇒ \(n - 1 = -65 \times\frac{-2}5 = 26\) ⇒ \(n = 26 + 1 = 27\) Hence, 27th term of given A.P. will be -47. |
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