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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:
Two APs have the same common difference. The first term of one of these is $–1$ and that of the other is$ – 8$. Then the difference between their $4^{th}$ terms is:
  • A
    $-1.$
  • B
    $-8$
  • ✓
    $7$
  • D
    $-9$
✓

Answer

Correct option: C.
$7$
Let the common diference of two $AP$ s are $d _1$ and $d _2$, respectively.
Bycondition, $d _1= d _2= d$
Let the first term of first AP $\left(a_1\right)=-1$
and the first term of second $A P\left(a_2\right)-8$
we know that, the $n^{\text {th }}$ term of an $A P, T_1=a+(n-1) d$
$\therefore 4^{\text {th }}$ term of first $A P, T_4=a+(4-1) d=-1+3 d$
and $4^{\text {th }}$ term of second $A P, T_4=a_2+(4-1) d=-8+3 d$
Now, the difference between there $4^{\text {th }}$ term is i.e.,
${\left[T_4-T^{\prime} 4\right]=(-1+3 d)-(-8+3 d)}$
$=-1+3 d+8-3 d=7$

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