Find the first term, the common difference, and give a recursive formula for the arithmetic sequence.
-6th term is -10; 15th term is -46
A) a1 = 10, d = 4, an = an-1 + 4
B) a1 = -10, d = -4, an = an-1 - 4
C) a1 = -30, d = 4, an = an-1 + 4
D) a1 = 10, d = -4, an = an-1 - 4

Question

Quizplus · Accepted Answer

The common difference (d) can be found using the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n-1)d$. Given the 6th term is -10 and the 15th term is -46, we can set up two equations: $a_1 + 5d = -10$ and $a_1 + 14d = -46$. Subtracting the first equation from the second gives $9d = -36$, so $d = -4$. Substituting $d = -4$ into $a_1 + 5(-4) = -10$ gives $a_1 + (-20) = -10$, so $a_1 = 10$. The recursive formula for an arithmetic sequence with a common difference of -4 is $a_n = a_{n-1} - 4$.

Find the First Term, the Common Difference, and Give a Recursive