The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is 170 . If there are at least 6 houses in that row and a is the number of the sixth house, then

Step-by-step solution

Let house no are , ,+2, +4, +6, +8, +10, . +10=a =a-10 ...... (1) House no. will be (+) array l =a-10>0 >10 12 as a is each too ...... (2) array Now S_ n = n 2 [2 +(n-1) d] array l 170= n 2 [2 +(n-1)(2)] =n( +(n-1)) =n(a-10+n-1) =n(a-11+n) n²+n(a-11)-170=0 n= (11-a) (a-11)²+680 2 ...... (3) n 6 (11-a) (a-11)²+680 2 6 a 800 24 ...... (4) array From (2) and (4) 12 a 32 Now checking through (3) for a=12,14, . . ; we have a=18, n=10 and S_ n =170