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Arithmetic Progressions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsArithmetic Progressions1 Mark
MCQ
Mark the correct alternative in the following:Two $A.P.$'s have the same common difference. The first term of one of these is $8$ and that of the other is $3$. The difference between their $30_{th}$​​​​​​​ term is:
  • A
    $11$
  • B
    $3$
  • C
    $8$
  • ✓
    $5$
✓

Answer

Correct option: D.
$5$
In two $A.P.$'s common difference is same
Let $A$ and a are two $A.P.'s$
First term of A is $8$ and first term of a is $3$
$A_{30} - a_{30} = 8 + (30 - 1)d - 3 - (30 – 1)d$
$= 5 + 29d - 29d = 5$

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