The fourth term of a particular infinite arithmetic sequence is 203 and the thirteenth term is 167. What is the smallest value of đť‘› such that the đť‘› th term of the sequence is negative?
203==F + 3D,
167 ==F + 12D, solve for F, D
F==215 - this is the first term
D == - 4 - this is the common difference
round(215/ - 4) + 1 ==55th term - when negative term first appears.
Your AP will look like this:
215 , 211 , 207 , 203 , 199 , 195 , 191 , 187 , 183 , 179 , 175 , 171 , 167 , 163 , 159 , 155 , 151 , 147 , 143 , 139 , 135 , 131 , 127 , 123 , 119 , 115 , 111 , 107 , 103 , 99 , 95 , 91 , 87 , 83 , 79 , 75 , 71 , 67 , 63 , 59 , 55 , 51 , 47 , 43 , 39 , 35 , 31 , 27 , 23 , 19 , 15 , 11 , 7 , 3 , -1 , >>Number of terms = 55>>Total Sum == 5885
