An A.P consists of 50terms of which 3rd term is 12 and the last term is 106 . find the 29th term .

An A.P consists of 50terms of which 3rd term is 12 and the last term i

1.	An A.P consists of 50terms of which 3rd term is 12 and the last term is 106 . find the 29th term .
Answer» Let the first term and the common difference of the AP be a and d respectively.3rd term = 12 ..... Given{tex} \\Rightarrow {/tex}\xa0a + (3 - 1)d\xa0= 12\xa0{tex}\\because {a_n} = a + (n - 1)d{/tex}{tex} \\Rightarrow {/tex}\xa0a + 2d = 12 ......... (1)Last term = 106 ........ Given{tex} \\Rightarrow {/tex}\xa0So the term = 106\xa0{tex}\\because {/tex}\xa0The AP consists of 50 terms{tex} \\Rightarrow {/tex}\xa0a + (50 - 1)d = 106{tex} \\Rightarrow {/tex}\xa0a + 49d = 106 ........ (2)Solving (1) and (2), we geta = 8d = 2Therefore, 29th term of the AP= 9 + (29 - 1)d\xa0{tex}\\because {a_n} = a + (n - 1)d{/tex}= 9 + 28d= 8 + (28) (2)= 8 + 56= 64