00:01
In this problem of sequence and series we have given the a 8 that means 8th term of the series that is 26 and 12 term of the series that is 812 equals to 42 and now we have to find the first five terms of the sequence so this is a n that is the nth term of the sequence is given by a plus n minus 1 with the common difference where a is equal to where a is equal to a1 and now put here a 8 put here n is equal to 8 so this would be a plus 8 minus 1 that is 7d which is equal to 26 and we have given a 12 put here n is equal to 12.
00:39
So this would be a plus 11 d that is 12 minus 1d equals to 42 and now subtract it.
00:46
So this would be minus minus minus so this 8 terms get cancelled and we have minus 4d is equal to this is minus 42 minus 4d 2 here this is minus 4d 2.
00:58
2 plus 26 which is equals to 16 so this is here minus 16 which is this is equals to minus 16 that means 6 here minus to minus gets cancelled and d is equal to 16 divided with 4 which is equal to 4 and we have value of here d is 4 and we have to find the value of a now put here a plus 7d is equal to we have given a plus 7d is equal to 26 put here d is equal to 4 so so this would be a plus 7 multiplied with 4, that is 28, which is equal to 26, and a is equal to 26 minus 28, 26 minus 28, which is equal to minus 2.
01:43
So we have the value of a1 is equal to a, that is minus 2.
01:47
So a1 is equal to a which is minus 2 and now a2.
01:52
Put here n is equal to 2, so this would be a plus 2 minus 1 d, that is d.
01:57
So, a is equal to 2 and d is equal to 4 which is equal to 2...