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  • If the common difference of an AP is 5, then what is a18 – a13? (A) 5 (B) 20 (C) 25 (D) 30

If the common difference of an AP is 5, then what is a\textsubscript{18} - a\textsubscript{13}?

(A) 5

(B) 20

(C) 25

(D) 30

Answers (1)

Given

d = 5 \\ a_{18} - a_{13} = ? \\ \text{We know that } a_n = a + (n - 1) \cdot d \\ \text{Put } n = 18, \quad a_{18} = a + (18 - 1) \cdot d \\ \text{Put } n = 13, \quad a_{13} = a + (13 - 1) \cdot d \\ \text{Now } a_{18} - a_{13} = (a + (18 - 1) \cdot d) - (a + (13 - 1) \cdot d) \\ = a + 17d - a - 12d \\ = 17d - 12d \\ = 5d \\ = 5 \times 5 \\ = 25

Option is (C) is correct.

Posted by

infoexpert21

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