The 14th term of an AP is 202, and the 19th term of an AP is 277. Find the ratio of the series's first term and the 8th term.
Solution
Let the first term be "a" and the common difference of the AP be "d".
So, 14th terms of AP will be a+13d.
a+13d = 202 ----equation (1)
19th term of AP will be a+18d.
a+18d = 277 --------equation (2)
solving both equations, we get a = 7 and d = 15
Therefore, first term = 7
8th term = a+7d = 7+7*15 = 112
So, ratio = 7:112 = 1:16
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