find the 20th term from the end of the ap 3,8,13 253 - Maths - Arithmetic Progressions

Question

find the 20th term from the end of the ap 3,8,13 253

Aakash Sharma · Accepted Answer

The given AP series is 3, 8,13, 18, , 253 The first term a = 3 and common difference d = 8 â€“ 3 = 5 Let us first calculate the number of terms in the given series $a_{n} = a + (n - 1) \cdot d \Rightarrow 253 = 3 + (n - 1) \cdot 5 \Rightarrow 250 = 5 (n - 1) \Rightarrow n - 1 = 50 \Rightarrow n = 51$ Therefore, there are 51 terms 20th term from the end is $(51 - 20 + 1)$ th term $= 32$ th term from the beginning Therefore, $a_{32} = a + (32 - 1) \cdot 5 = 3 + 31 \cdot 5 = 3 + 155 = 158$ So, the 20th term from the end will be 158

find the 20th term from the end of the ap 3,8,13.......253