Sequence Differs !

-10 = -10 +0

-7 = -10 + 3

-2 = -10 + 3 + 5

5 = -10 + 3 + 5 + 7

14 = -10 + 3 + 5 + 7 + 9

so , next term = -10 + 3 + 5 + 7 + 9 + 11 = 25 :)

The difference between the terms increases by $2$ every time starting at $1$ when $k = 0$ so that means that

$a_k = a_{k - 1} + 2k - 1$

We're looking for the value when $k = 6$ so lets put that into our formula

$a_6 = a_{6 - 1} + 2(6) - 1$

Since $a_{6 - 1} = a_5$ and we know that $a_5 = 14$ from the question we can substitute to get

$a_6 = 14 + 12 - 1$

Which means that

$a_6 = 25$

Let the number be x

-7-(-10)=-7+10=3

-2-(-7)=-2+7=5

5-(-2)=5+2=7

14-5=9

Therefore,

x-14=11

=> x=25

as we take diff. between 2 terms like, diff of 2rd term and 1nd term... ans=3 btw 3&2 ans=5 btw 4&3 ans=7 btw5&4 ans=9 conclusion the answers are in AP with comm. diff 2 therefore next term will me 14+11=25