Progression Practice Test 1

Concept:For an arithmetic progression (AP), the $n$th term is given by $a_n = a + (n-1)d$, where $a$ is the first term and $d$ is the common difference.Explanation:Given AP: $11, 17, 23, \ldots$First term $a = 11$.Common difference $d = 17 - 11 = 6$.Let the term equal to $71$ be the $n$th term.So, $a_n = 71$.Substitute values in the formula:$11 + (n-1)6 = 71$.Simplify: $11 + 6n - 6 = 71$.Combine constants: $6n + 5 = 71$.Subtract $5$ from both sides: $6n = 66$.Divide by $6$: $n = 11$.Thus, $71$ occurs at the $11$th position.Check: $11$th term $= 11 + (11-1)6 = 11 + 60 = 71$.Answer:The required term is the $11$th term, so the correct option is E.