Explanation

The problem is an A.P.

$11, 13, 15$

given:$a = 11, Sn = 551$

to find $n = ?$ $d = 13 - 11$ $= 2$

using

$Sn = {n\over2}[2a + (n-1)d]$

$551 = n/2[2 \times 11 + (n-1)2]$

$1,102 = n(22 + 2n -2)$

$1102 = n(20 + 2n)$

$1102 = 20n + 2n^2$

$n^2 + 10n - 551 = 0$

$(n-19)(n+29) = 0$

$n = 19, or n = -29$

$thus: there are 19 houses$

The problem is an A.P.

$11, 13, 15$

given:$a = 11, Sn = 551$

to find $n = ?$ $d = 13 - 11$ $= 2$

using

$Sn = {n\over2}[2a + (n-1)d]$

$551 = n/2[2 \times 11 + (n-1)2]$

$1,102 = n(22 + 2n -2)$

$1102 = n(20 + 2n)$

$1102 = 20n + 2n^2$

$n^2 + 10n - 551 = 0$

$(n-19)(n+29) = 0$

$n = 19, or n = -29$

$thus: there are 19 houses$