Explanation

Examining the repeating pattern, you see that the 3rd term is 4, and every 3rd term after that, in other words, the 6th, 9th, 12th, 15th, and so on, is 4. Since 150 is a multiple of 3, the 150th term is 4. Therefore the 150th to the 154th terms are 4, 1, –3, 4, 1. The sum of these 5 terms is 7, so the correct answer is 7.
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150 is also a multiple of 2 and 5. How did you get 3 instead of 2 or 5 in this case?

Write out the sequence:

1, –3, 4, 1, –3, 4

6th term is 4 even though 6 is divisible by 2. We divided by 3 because there are 3 different types of numbers in the list.

For example lets take the following repeating sequence:

2, 5, 7, 8, 9, 2, 5, 7, 8, 9, 2, 5, 7, 8, 9, .....

What is the 15th number? 9 remainder of(15/5)= 0

what is the 22nd number? 5 remainder of (22/5)= 2


So you can vizualize the problem as follows:

remainder 1	remainder 2	remainder 3	remainder 4	remainder 0	remainder 1	remainder 2	remainder 3	remainder 4	remainder 0
2	5	7	8	9	2	5	7	8	9

Does this help?
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no of triplets(since 1,-3,4 keeps repeating) upto 150th place=150/3==>50
there are 50 triplets consisting of digits 1,-3,4
1st triplet=[1,-3,4]
2nd triplets=[1,-3,4]
.
.
.
50th triplets=[1,-3,4]
148th=1
149th=-3
150th=4
but we have t find the sum of [150th+151th+152th+153th+154th]
=4+1+(-3)+4+1
=10-3
=7