CAT 2017 Progression Question (Hard)

Question

Let be an arithmetic progression with and . If , then what is the smallest positive integer such that ?

Accepted Answer

Step 1 We are given - - - Common difference - Number of terms - Total sum of terms S_ 3n 1830 Sum of AP S_ 3n 2 left 2a_1 3n - 1 d right Substitute 1830 2 left 2 times 3 3n - 1 times 4 right Compute Thus 1830 2 6 12n - 4 2 12n 2 Simplify So 1830 2 times 2 6n 1 3n 6n 1 Therefore 3n 6n 1 1830 Divide b

CAT 2017

Quantitative

Progression

Hard

Let $a_1, a_2, \ldots, a_{3n}$ be an arithmetic progression with $a_1 = 3$ and $a_2 = 7$ . If $a_1 + a_2 + \ldots + a_{3n} = 1830$ , then what is the smallest positive integer $m$ such that $m(a_1 + a_2 + \ldots + a_n) > 1830$ ?

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