Question 1196371: Which term of the arithmetic sequence -10,-6,-2,2,6.... i s 94? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52788) (Show Source):
Use the formula for the n-th term of an AP
= + (n-1)*d.
In your case = -10, d = 4, = 94.
So, your equation is
94 = -10 + (n-1)*4.
It gives
94 + 10 = 4(n-1)
104 = 4(n-1)
n-1 = 104/4 = 26
n = 26 + 1 = 27.
ANSWER. 27-th term.
You should understand the formal algebraic solution shown by the other tutor.
However, using formulas blindly doesn't teach you much about the actual problem. You should be able to use logical reasoning and simple arithmetic to get the answer (and to see why the formal solution gives the right answer).
The difference between -10 and 94 is 104; the common difference is the difference between -10 and -6, which is 4. 104/4 = 26; so 94 is 26 terms after the first term, making it the 27th term.
