Question

What is the next number in the sequence 1,5, 14,30, 55, 91

Answer 1

140

Answer 2

explain

Answer 3

we have
1, 5, 14, 30, 55, 91
5-1=4=2^2
14-5=9=3^2
30-14=16=4^4
55-30=25=5^2
91-55=36=6^2
so the difference between two consecutive no. is the square of nth term
91 is the 6th term,
7th term is =91+7^2=91+49=140

Answer 4

hey the 30-14 one doesnt fit in

Answer 5

30-14=16=4^2
30 is the 4th term, generated by 4^2+14

Answer 6

sorry I wrote 4^4, it's 4^2

Answer 7

so ash hw to approach such ques?

Answer 8

tanu, if you are given a sequence, first check , the difference between consecutive terms,
Is it a sequence or is it similar?
or check the difference between the differences itself, sometimes it may be a pattern.
in some cases alternate terms have a pattern like
1, 2, 5, 6, 9, 10
here 1, 5, 9, generated by adding 4 to the term before the previous
2,6 ,10 are a series

Answer 9

how do u check for a a.p /g.p

Answer 10

AP will have a common term added to each term to generate the next term
1, 3, 5, 7
1+2=3
3+2=5
5+2=7

and so on
GP will have a common term multiplied to generate the next term
2, 6, 18, 54, 162
6=2*3
18=6*3
54=18*3
162=54*3
and so on
note that term added or multipled can either be a positive or negative no. . No restriction on this , can be a irrational no. also

Answer 11

thanks

Answer 12

glad to help:)