Question

an ap consist of 50 terms of which 3rd term is 12 and the last term is 106 find the 29th term
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Answer 1

Step-by-step explanation:

Given: In an AP,

1. number of terms=50.
2. A3=12 => a+2d=12.----(1)
3. Last term,l=106. => a50=106 => a+49d=106.----(2).

To find: a29 = ?

By (2)-(1), we get:

=> a+49d-(a+2d)=106-12

=> a+49d-a-2d=94.

=> 47d=94

=> d=94/47

=> d=2.----(3)

By substituting (3) in (1):

=> a+2(2)=12

=> a=12-4

=> a=8.

Formula of nth term:

$an = a + (n - 1) \times d$

=> a29=8+(29-1)×2

=> 8+28×2

=> 8+56

=> 58.