GATE (TF) Textile 2014 Question Paper Solution | GATE/2014/TF/27

Question (Textile Engineering & Fibre Science)

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Arithmetic sequences-
15,19,23,………………………..
and
14,19,24,………………………

First common term=19
Second common term=39
Third common term=59

Series of common terms-
19,39,59,…………………………
Value of 51th common term
$T_51=19+(51-1)\times 20$
$T_51=19+50\times 20$
$T_51=19+10000$
$T_51=1019$ (Ans)

To calculate no. of common terms method-
Arithmetic sequences-
15,19,23,…………….
$a_n=15+(n-1)\times 4$
$a_n=4n+11$
and

14,19,24,………………
$a_n=14+(m-1)\times 4$
$a_n=4m$
Here,
$a_n=a_m$
$4n+11=4m=k(Let)$
$n+\frac{11}{4}=m=k$
For 51th common term-
$n+\frac{11}{4}<51$
$n<48.25$
and
m<51
so, 48 terms are common.

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