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The fourth term of a particular infinite arithmetic sequence is 203 and the thirteenth term is 167. What is the smallest value of 𝑛 such that the 𝑛 th term of the sequence is negative?

 Dec 16, 2021
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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

 Dec 17, 2021
edited by Guest  Dec 17, 2021

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