-3(+2)=-1
-1(+12)=11
11(+28)=39
39(+50)=89
Now look at the addition sequence,
2(+10),12(+16),28(+22),50 so next addition is
50(+28)=78
so next term is
89+78=167....Ans

question is based on triangular pattern series
ie.,
-3 -1 11 39 89 x (x is to be found)
2 12 28 50 y (y=x-89)
10 16 22 z (z=y-50)
now last series is in AP with d=6,
therefore z= 28
by backward substitution, we get x=167

The given sequence is...

-3,-1,11,39,89,...... ---------> sequence 1

if u will subtract -1 - (-3), 11 - (-1),39-11,89-39
you will get the sequence as 2,12,28,50 ---> seq 2

now again if u will subtract 12-2,28-12,50-28

you will get the sequence as 10,16,22 ----->seq 3

now you can see that the common difference in sequence 3 is 6
..now you can calculate from there that after 22
what will be the next number.
The next number will be 22+6=28

now we have 10,16,22,28 as sequence 3

now we have sequence 2 as 2,12,28,50

we know that last number of sequence 3 is 28 so
the next number of sequence 2 will be 50 + 28=78

now we have sequence 2 as 2,12,28,50,78

we know that the sequence 1 is -3,-1,11,39,89
and the last number of sequence 2 is 78

so the next number of sequence 1 will be 89+78=167

Therefore correct answer will be 167

each term is given by
x^3-x^2-2x-1

where x=1,2,3,4,5,6
when x=6,
6th term = 216-36-2*6-1 =167

nth term is given by
n^3 -(n+1)^2
when n=1, term = 1^3-2^2=-3
when n=2, 2nd term = 2^3-3^2=-1
..
..
T6= 6^3-7^2=216-49=167 .. option 5

each diff is 10 16 22 next 28
so 89 + 78=167

-3 ,-1 ,11, 39 ,89,..
difference 2 12 28 50
difference 10 16 22 28
therefore 28+50+89=167

given series is -3,-1,11,39,89
1st differece series -1+3=2
2,12,28,50
2nd difference series=10,16,22
third difference=6,6
backtrack 22+6=28
50+28=78
89+78=167
ans=167

-3 -1 11 39 89 x
2 12 28 50 y
10 16 22 z
6 6 6
therefore, z=22+6=28
y=28+50=78
x=78+89=167

a(n)=n^3-(n+1)^2.
a(1)=1^3-(1+1)^2=-3
a(2)=2^3-(2+1)^2=-1
a(3)=3^3-(3+1)^2=11
a(4)=4^3-(4+1)^2=39
a(5)=5^3-(5+1)^2=89
a(6)=6^3-(6+1)^2=167

-3,-1,11,39,89,167
-1-(-3) = 2
11-(-1) = 12
39-11 = 28
89-39 = 50
167-89 = 28
now difference between differences:
12-2 = 10
28-12 = 16
50-28 = 22
78-50 = 28
again difference between differences:
16-10 = 6
22-16 = 6
28-22 = 6

differences of no. are varry like this
2*1=2
3*4=12
4*7=28
5*10=50
so,
6*13=78
89+78=167

given series is -3,-1,11,39,89,x...
-1-(-3)=2,11-(-1)=12,39-11=28,89-39=50
series is 2,12,28,50,...----->(1)
12-2=10,28-12=16,50-28=22
series formed is 10,16,22,.. next no is 28(22+6)
next no for series 1 is 50+28=78
next no for given series is 78+89=167

Sum of differnce of last two numbers is 78/2=39 and multiply it with 2 so 78 and adding to 89 gives the answer 167.

-3 -1 11 39 89 167
2 12 28 50 78
10 16 22 28
6 6 6

Differences :
First Level : 2, 12, 28, 50.
Second Level : 10, 16, 22.
Third Level : 6, 6
Hence next second level difference is 22+6 = 28.
Hence next first level difference is 50+28 = 78.
Hence the required number is 89+78 = 167.
Hence option no. (5)

-3+2=-1
-1+12=11
11+28=39
39+50=89
here we see that 12-2=10
28-12=16
50-28=22
so here 10,16.22 are in A.P so next will be 28 i.e 50+28=88
in the same way 89+88=167 ans

the series are in (n^3)-((n+1)^2)...
Substituting 1,2,3.... we get the series... :) :)

ans is 167
crct option is 5

nth term = (n-1)th term + n(3n-5)
for eg, 2nd term =1st term+(2*1)
5th term = 4th term + 5*10
so next term is
89 + 6*13 = 167

adding 2 ,12, 28, 50, 78.

triangular format..

a(n)= n^3 - (n+1)^2

n = 1
n= 1-4 =-3
So on...
n=6
n= 216 - 49. = 167

series is -3,-1,11,39,89
differences- 2,12,28,50,...it also can be a series
now differences for series of differences
10,16,22
it is maintaining a difference of 6
so next number in series of differences will be 50+28=78
So next term of original series= 89+78=167

-3 -1 11 39 89 167
2 12 28 50 78
10 16 22 28

ans is 167

there is two level difference ....
-3,1,11,39,89 and their differences are
2,12,28,50
and here the differences of the difference is
10,16,22 with the difference of 6
so the next number will be at second level is 28
i.e last number at first level difference will be 50+28=78
so the next number of the sequence will be
89+78= 167.

difference bet -1 & -3 = 2
11 & -1 = 12
39 & 11 = 28
89 & 39 = 50
new series: 2 12 28 50
difference bet 12 & 2 = 10
28 & 12 = 16
50 & 28 = 22
next diff should be 28
hence next number in new series will be 78
so, next number in given series will be 89 + 78 = 167

Difference b/w each 2 no. is 2,12,28,50
then diffn b/w this 4 no. is 10,16,22 and diffn b/w this 3 no. is 6....so next no. is 89+(22+6+50)=167

1^3-2^2=-3
2^3-3^2=-1
3^3-4^2=11
4^3-5^2=11
5^3-6^2=89
6^3-7^2=167

diff 2 12 28 58
next diff 10 16 22
next diff 6 6
next 1
so next number is(89+(50(22+6)))

differences between numbers 2,12,28,50 respectively..and the difference between these is 10 ,16,22...by observing this the later is 28..so add 28 to the previous series...we get 78...now add 78 to 89...the result is 167
therefore the Answer is 167.