Algebra

Arithmetic Progressions

Arithmetic Progressions - Problem Solving

         

Non-zero numbers a,b,c,d,e a, b, c, d, e form an arithmetic progression. If b+d2+a+e4=kc, \frac{b+d}{2} + \frac{a+e}{4} = kc, find the value of k k .

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Two sequences {x,a1,a2,a3,y} \{ x, a_1, a_2, a_3, y \} and {x,b1,b2,b3,b4,b5,y} \{ x, b_1, b_2, b_3, b_4, b_5, y \} each form an arithmetic progression. If x≠y x \neq y , what is the value of

a2−a1b5−b4? \frac{a_2 - a_1}{b_5 - b_4} ?

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For an arithmetic progression {an} \{a_n\} , the following equalities hold: a3+a5=36,a2a4=180. a_3 + a_5 = 36, \quad a_2 a_4 = 180.

Find the largest n n such that an<100. a_n < 100.

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An arithmetic progression {an} \{a_n \} satisfies a2+a4+a6+⋯+a2n=2n2+3n. a_2 + a_4 + a_6 + \cdots + a_{2n} = 2n^2 + 3n. Find the value of a3+a6+a9+⋯+a18. a_3 + a_6 + a_9 + \cdots + a_{18}.

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For an arithmetic progression {an} \{ a_n \} , a3=8 a_3 = 8 and a10=29a_{10} = 29 . If an=200 a_n = 200 , what is n?n ?

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