Find the eleventh term from the last term of the AP: 27, 23, 19, ..., –65.

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Question 3 Find the eleventh term from the last term of the AP: 27, 23, 19, ..., –65.AP is 27, 23, 19, ……, –65 Here a = 27 d = 23 – 27 = –4 First lets find which term is –65 Let an = – 65 a + (n – 1) d = – 65 Putting values 27 + (n – 1) ( –4) = – 65 27 + n (–4) – 1(–4) = – 65 27 – 4n + 4 = – 65 27 – 4n + 4 = – 65 31 – 4n = – 65 –4n = – 65 – 31 –4n = –96 n = (−96)/(−4) n = 24 We need to find out 11th term from the last term Last term = 24th Second last term = 24 – 1 =23th Third last term = 24 – 2 = 22nd And so, on So, 11th from last term = (24 – 10)th term . = 14th term So, we need to find out a14 an = a + (n – 1) d Putting values a14 = 27 + (14 – 1) (–4) a14 = 27 + (13) (–4) = 27 – 52 = –25 So, 11th term from the last = 14th term from the first = –25

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