Sequence

Unless the type of the sequence is mentioned the first term cannot be determined uniquely. Please check the question again. I believe there it is mentioned as an arithmetic progression.

Aman verma wrote:Q: In a sequence which is an arithmetic progression in descending order, sum of all its terms , except for the first term , is equal to -36, the sum of all its terms,except for the last term, is zero, and the difference of the tenth and the sixth term is equal to -16, then what will be the first term of this sequence

Say, the first term is a and the common difference is d and there are n terms in total.
Hence, tenth term = (a + 9d) and sixth term = (1 + 5d)
Therefore, (a + 9d) - (a + 5d) = -16 ---> d = -4

Last term, i.e. n-th term = a + (n - 1)d

Now, first term - last term = 36
---> a - a + (n - 1)d = 36
---> -(n - 1)d = 36
---> n = 10

Now sum of first 9 terms is equal to zero. As these 9 terms are uniformly spaced, their average must be equal to their median, i.e. the 5th term will be equal to zero. Hence, (a + 4d) = 0 ---> a = -4d = 16

The correct answer is A.