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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions1 Mark
MCQ
Choose the correct answer from the given four options: What is the common difference of an $AP$ in which $a_{18}-a_{14}=32 ?$
  • ✓
    $8$
  • B
    $-8$
  • C
    $-4$
  • D
    $4$
✓

Answer

Correct option: A.
$8$
$\text { Given, } a_{18}-a_{14}=32$
${\left[\therefore a_n=a+(n-1) d\right]}$
$\Rightarrow a+(18-1) d-[a+(14-1) d=32$
$\Rightarrow a+17 d-a-13 d=32$
$\Rightarrow 4 d=32$
$\Rightarrow d=8$
which is the required common difference of an $AP.$

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