First slide

Arithmetic progression

Question

$The largest term common to the sequences 1,11,21,31,… to 100 terms and 31,36,41,46,… to 100 terms is$

Difficult

A

381
B

471
C

281
D

521

Solution

$\begin{array}{l} t_{m} = t_{n} \\ 1 + (m - 1) 10 = 31 + (n - 1) 5 \\ \Rightarrow m = \frac{n + 7}{2} = λ \\ \Rightarrow m = λ, n = 2 λ - 7 \\ \Rightarrow m \leq 100, n \leq 100 \\ 2 λ - 7 = 100 \\ 2 λ \leq 107 \\ λ = 53 \end{array}$
$number of common terms are 53$
$the largest common term is t_{53} = 1 + 52 \times 10 = 521$

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