rakaisraka wrote:Each term in the sequence A1 +A2 + A3 ----- + An is either 7 or 77 and th sum equals 350. What could be the value of n.
a) 38
b) 39
c) 40
d) 41
e) 42
The above solutions are faster. However, if you didn't spot them, another approach is to look for a pattern.
The sum of any 1 term will have units digit
7
The sum of any 2 terms will have units digit 4
The sum of any 3 terms will have units digit 1
The sum of any 4 terms will have units digit 8
The sum of any 5 terms will have units digit 5
The sum of any 6 terms will have units digit 2
The sum of any 7 terms will have units digit 9
The sum of any 8 terms will have units digit 6
The sum of any 9 terms will have units digit 3
The sum of any 10 terms will have units digit 0
The sum of any 11 terms will have units digit
7 (
at this point, the pattern repeats)
From this, we can conclude that the sum of any 20 terms will have units digit 0
And the sum of any 30 terms will have units digit 0, and so on.
We are told the sum of the terms is 350 (units digit 0), so the number of terms must be 10 or 20 or 30 or . . .
Since
C is a multiple of 10, this must be the correct answer.
Cheers,
Brent
