the sum of 6 consecutive odd numbers is 200. What is the fourth number in this sequence?

解

t h e s u m o f 6 co n sec u t i v e o dd n u mb ers i s 200. Wha t i s t h e f o u r t h n u mb er in t hi s se q u e n ce ?

解なし

解答ステップ

Represent the numbers with

x

First number : x

Consecutive number 1 : x + 2

Consecutive number 2 : x + 4

Consecutive number 3 : x + 6

Consecutive number 4 : x + 8

Consecutive number 5 : x + 10

A.T.Q.:

x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 = 200

解く

x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 = 200 : x = \frac{85}{3}

x + 2 = \frac{85}{3} + 2 = \frac{91}{3}

x + 4 = \frac{85}{3} + 4 = \frac{97}{3}

x + 6 = \frac{85}{3} + 6 = \frac{103}{3}

x + 8 = \frac{85}{3} + 8 = \frac{109}{3}

x + 10 = \frac{85}{3} + 10 = \frac{115}{3}

Even value

\frac{85}{3}

discarded

解なし