What is the best solution for exercise 5.2 of chapter arithmetic progressions of math, how i solve easily this question because it is very important type of question An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
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An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term. Q.8
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Given that,
3rd term, a3 = 12
50th term, a50 = 106
We know that,
an = a+(n−1)d
a3 = a+(3−1)d
12 = a+2d ……………………………. (i)
In the same way,
a50 = a+(50−1)d
106 = a+49d …………………………. (ii)
On subtracting equation (i) from (ii), we get
94 = 47d
d = 2 = common difference
From equation (i), we can write now,
12 = a+2(2)
a = 12−4 = 8
a29 = a+(29−1) d
a29 = 8+(28)2
a29 = 8+56 = 64
Therefore, 29th term is 64.