In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560.?

Question

What is the sum of the last 5 integers in the sequence?

How do you get the conclusion?

Answer 1

Let x be the first consecutive integer.

We have:

x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 560

We want:

(x + 5) + (x + 6) + (x + 7) + (x + 8) + (x + 9)

So it comes down to solving for x.

Simplifying the first equation by grouping like terms, we get

5x + 10 = 560
5x = 550
x = 110

The second expression for the last 5 integers simplifies to
5x + 35, so with x = 110,

5x + 35 = 5(110) + 35 = 550 + 35 = 585.

The last 5 integers add up to 585.

Answer 2

Let x be the first consecutive integer.
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 560
(x + 5) + (x + 6) + (x + 7) + (x + 8) + (x + 9)
So it comes down to solving for x.
Simplifying the first equation by grouping like terms, we get
5x + 10 = 560
5x = 550
x = 110
The second expression for the last 5 integers simplifies to
5x + 35, so with x = 110,
5x + 35 = 5(110) + 35 = 550 + 35 = 585.

Answer 3

let x = first integer, x+1 = second, x+2 = 3rd, x+3 = 4th, x+4 = 5th

x + x+1 + x+2 + x+3 + x+4 = 560
5x + 10 = 560
5x = 550
x = 550/5
x = 110

The next 5 integers would be x+5, x+6, x+7, x+8, and x+9
x+5 + x+6 + x+7 + x+8 + x+9 = sum of last 5 intergers of sequence
5x + 35 = sum of last 5 integers of sequence
since we know x = 110
5(110) + 35 = sum of last 5 integers of sequence
550 + 35 = sum of last 5 integers of sequence
sum of last 5 integers of sequence = 585

answer is 585

Answer 4

let 1 number = x ,
then the other 9 are x+1 , x+2 , x+3 , x+4 , x+5 ,x+6,x=7,x=8,x=9

first 5 integers = x ,x+1,x=2,x=3,x=4
according to question
x+x+1+x2+x+3+x+4=560
5x+10=560
5x=560-10
5x=550
x=550/5
x=110

last 5 integers = x+5,x+6,x+7,x+8,x+9
sum of last 5 integers =x+5+x+6+x+7+x+8+x+9
=5x+35
=(5*110)+35
=550+35
=585

Answer 5

585.

They are consecutive integers.
Let x be the first integer so the sum of the first 5 is:

x + (x+1) + (x+2) + (x+3) + (x+4) = 560
5x + 10 = 560
5x = 550
x = 110

The numbers are:

110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Answer 6

585

the sum of the first five integers plus 5x5 or the difference of the next five integers minus the first five integers. They increment by 5 each.

Answer 7

585

In the last five, there is a number five greater than in the first five. 5x5 = 25, so the second five add to 560+25=585. You don't need to solve for x.