Identify the 42nd term of an arithmetic sequence where a1=-12 and a27=66.

Question

campbell_st · Answer

you need to find the common difference d

using the 27th term 

$$T _{27} = -12 + (27 -1)d$$

or $$66 = -12 + 26d$$

solve for d

then evaluate the formula with n = 42

anonymous · Answer

$$a(n) = a(1) + (n - 1)d$$
$$a(1) = -12$$a(n) = -12 + (n - 1)d
$$a(27) = 66$$66 = -12 + (27 - 1)d
$$66 = -12 + 26d$$
$$26d = 66 + 12$$
$$26d = 78$$
$$d = 78/26$$
$$d = 3$$
$$a(n) = -12 + 3(n - 1)$$
$$a(42) = -12 + 3(42 - 1) = -12 + 3(41) = -12 + 123 = 111$$