Maths / Arithmetic Progression / Find The Value of Nth Term when Common Difference, Number of Terms and First Term are Given

QUESTION

Which  term of the AP 1, 5, 9, 13, ......... is 405?

 OPTIONS A. $\dpi{100} 103^r^d$ B. $\dpi{100} 105^t^h$ C. $\dpi{100} 117^t^h$ D. $\dpi{100} 102^n^d$
Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

For the given AP a = 1, a + d = 5 or d = 4

Let                    $\dpi{100} a_n$  = 405 $\dpi{100} \rightarrow$  a + (n - 1) d = 405

$\dpi{100} \rightarrow$             1 + (n - 1) (4) = 405  $\dpi{100} \rightarrow$  (n - 1) (4) = 404  $\dpi{100} \rightarrow$ n - 1 = 101

$\dpi{100} \rightarrow$                               n = 102

Thus the $\dpi{100} 102^t^h$ term is 405.

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