clarification needed

[selango]

OG 12 Prob 85

In an increasing sequence of 10 consecutive integers , the sum of 5 integers is 560.what is the. sum of last 5 intergers in the sequence?

A)585

B)580

C)575

D)570

E)565


The solution is given as x+x+1+x+2+x+3+x+4=560

My doubt is consecutive integers can be defined as x,x+d,x+2d,x+3d
where d is the difference.

But here it mentioned the consecutive integers with diff 1 like(1,2,3,4)But the difference can be anything like 2or 3 also

Is it correct?Please clarify

[liferocks]

x,x+d,x+2d,x+3d forms a AP with common difference as d
consecutive integers are in a AP where common difference is 1 i.e d=1

Hope this answers your question.

[selango]

But 11,13,15,18 (diff is 2) can also be defined as consecutive integers?is it right?

[indiantiger]

Here is the generic definition :
https://simple.wikipedia.org/wiki/Consecutive_integer

A series like 12,15,18,21
can be called evenly spaced. I hope this helps
please do correct me if I am wrong.

[krazy800]

But 11,13,15,18 (17 right) (diff is 2) can also be defined as consecutive integers?is it right?

Selango:

Unless mentioned, the consecutive integers are in A.P with a Common Difference (d) =1

ex 1,2,3,4,5

The numbers that u have used 11,13, 15, 17 are consective odd integers, not just the consective integers

Similarly 2, 4, 6, 8 Consective even integers

HTH!!!!