An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Explanation

Let the first term and common difference of the A.P. be 'a' and 'd' respectively.
`a_(3)=12 rArr a+2d=12 " " ...(1)`
`a_(50)=160 rArr a+49d=106 " " ...(2)`
Subtract eq. (1) from eq. (2), we get
`{:(" "a+49d=" "106),(underset(-)" "aunderset(-)""+2d=underset(-)" "12),(bar(" "47d=94" ")):}`
`rArr" " d=2`
put d=2 in eq. (1), we get
a+2(2)+12
`rArr a=8`
Now, `a_(29)=a+(29-1)d`
`=8+28xx2=64`