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  • What is the common difference of an AP in which a_18 – a14 = 32? (A) 8 (B) – 8 (C) – 4 (D) 4

What is the common difference of an AP in which a18 - a14 = 32?

(A)  8

(B) – 8

(C) – 4

(D)   4

Answers (1)

Given,

\\a\textsubscript{18 }- a\textsubscript{14} = 32 \\ $We know that a\textsubscript{n} $= a + (n - 1).d\\ $Put n $= 18\\ a\textsubscript{18} = a + (18 - 1).d\\ a\textsubscript{18} = 9 + 17d$ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ ..(1)\\ n = 14\\ a\textsubscript{14} = a + (14 - 1).d\\ a\textsubscript{14} = 9 + 13d$ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ .(2)\\ $subtract eq (2) from eq(1)\\$ a\textsubscript{18}- a\textsubscript{14} = 32\\ (a + 17d) - (a + 13d) = 32\\ a + 17d - a - 13d = 32\\ 4d = 32\\ d = \frac{32}{4} \\ d=8 \\

Hence common difference is 8.

Posted by

infoexpert21

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