Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions1 Mark
MCQ
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is:
✓
191
B
193
C
211
D
None of these
✓
Answer
Correct option: A.
191
191
Solution:
As, the common difference of the A.P. $3,7,11,15, \ldots=7-3=4$ and the common difference of the A.P. $1,6,11,16, \ldots$ $=6-1=5$ And, the common terms of both the A.P.s will be in A.P.
So, the common difference of the A.P. of the common terms, $d=\operatorname{LCM}(4,5)=4 \times 5=$ its first common term, $a=11$
Now, the tenth common term, $a_{10}=a+(10-1) d$
$=11+9 \times 20$
$=11+180$
$=191$
Hence, the correct alternative is option (a).
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