In a sequence of 10 increasing consecutive integers, the sum of the last five integers is 230.?

Question

What is the sum of the first 5 integers in the sequence?
A.205 B.210 C.215 D.220 E.225, whats answer and how or why?

Answer 1

x to x + 4 are the first 5.

x + 5 to x + 9 are the last 5.

The sum of the last 5 would be:

x + 5 + x + 6 + x + 7 + x + 8 + x + 9, or 5x + 35

The sum of the first 5 would be:

x + x + 1 + x + 2 + x + 3 + x + 4 = 5x + 10

So the sum of the first 5 is 35 - 10 = 25 less than the sum of the last 5.

230 - 25 = 205, answer A

Answer 2

x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8) + (x + 9)

(x + 9) + (x + 8) + (x + 7) + (x + 6) + (x + 5) = 230
5x + 35 = 230
5x = 195
x = 39

x + (x + 1) + (x + 2) + (x + 3) + (x + 4) =
5x + 10 = 5(39) + 10 = 195 + 10 = 205

ANS : A.) 205

Answer 3

Sn=(2a+(n-1)b)n/2

S10-S5=230
(2a+(10-1)*1)*10/2-(2a+(5-1)*1)*5/2 = 230
10a+45-(5a+10) = 230
5a + 35 = 230
5a = 195
a = 39

S5 = (2*39+(5-1)*1)*5/2
S5 = 5*39+%*2
S5 = 195 + 10
S5 = 205
The answer is A