The-solution-of-the-equation-x-1-x-4-x-7-x-28-155-is-given-by-x-

Question Number 110016 by ZiYangLee last updated on 26/Aug/20

The solution of the equation

(x + 1) + (x + 4) + (x + 7) + \dots + (x + 28) = 155

is given by x =_____.

Answered by Aziztisffola last updated on 26/Aug/20

10 x + 1 + 4 + 7 + \dots + 28 = 155

10 x + \frac{1 + 28}{2} \times 10 = 155

10 x + 5 \times 29 = 155

10 x + 145 = 155

10 x = 10 \Rightarrow x = 1

Commented by aurpeyz last updated on 26/Aug/20

pls how did you get 10 x in the first line ?

Commented by Aziztisffola last updated on 26/Aug/20

x + x + \dots + x = 10 x

\underset{\underset{10 terms}{⌣}}{1 + 4 + \dots + 28}

Answered by som(math1967) last updated on 26/Aug/20

x + x + \dots . 10 term + (1 + 4 + . . + 28) = 155

10 x + \frac{10}{2} {2 \times 1 + (10 - 1) \times 3} = 155

\Rightarrow 10 x + 145 = 155

∴ x = \frac{10}{10} = 1 ans

Answered by floor(10²Eta[1]) last updated on 26/Aug/20

notice that (1, 4, 7, . ., 28) is an AP with

ratio = 3

a_{n} = a_{1} + (n - 1) r

28 = 1 + (n - 1) 3 \Rightarrow n = 10

sum of the terms of a AP is

\frac{(a_{1} + a_{n}) n}{2} = \frac{(1 + 28) . 10}{2} = 145

∴ (x + 1) + (x + 4) + (x + 7) + \dots + (x + 28)

= 10 x + 145 = 155 \Rightarrow 10 x = 10 \Rightarrow x = 1

Commented by aurpeyz last updated on 26/Aug/20

h o w i s n u m b e r o f t e r m s e q u a l t o 10 ?

Commented by floor(10²Eta[1]) last updated on 27/Aug/20

3 and 4 line is the formula for the

general term of an AP