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8. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term |
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Answer» the 29th term is 64Step-by-step explanation:We know that the formula for the nth term is t N =a+(n−1)d, where a is the first term, d is the common difference.It is given that third term of an A.P is t 3 =12, therefore, t n =a+(n−1)d⇒12=a+(3−1)d⇒a+2d=12......(1)Also, it is given that the 50th term is t 50 =106, therefore, t n =a+(n−1)d⇒106=a+(50−1)d⇒a+49d=106......(2)Now, subtract equation 1 from 2 as FOLLOWS:(a−a)+(49d−2d)=106−12⇒47d=94⇒d= 4794 =2Substitute the value of the difference d=2 in equation 1:a+(2×2)=12⇒a+4=12⇒a=12−4=8Now, the 29th term with a=8 and d=2 can be obtained as:t 29 =8+(29−1)2=8+(28×2)=8+56=64 Hence, the 29th term is 64 |
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