MCQ
The $A.P$. whose third term is $16$ and the difference of $5^{th}$ term from the $7^{th}$ term is $12,$ then the $A.P$. is :
- A$\{4, 6, 8, 10,\}$
- B$\{4, 14, 24, 34,\}$
- ✓$\{4, 10, 16, 22,\}$
- D$\{4, 11, 18, 25,\}$
✓
Answer
Correct option: C.
$\{4, 10, 16, 22,\}$
Given : $a_3= 16$
$\Rightarrow a + 2d = 16 ... (i)$
And $a_7- a5 = 12$
$\Rightarrow a + 6d - a - 4d = 12$
$\Rightarrow 2d = 12$
$\Rightarrow d = 6$
Putting the value of d in eq. $(i),$ we get
$a + 2 \times 6 = 16$
$\Rightarrow a = 4$
$\therefore A.P$. is $\{4, 10, 16, 22,\}$
$\Rightarrow a + 2d = 16 ... (i)$
And $a_7- a5 = 12$
$\Rightarrow a + 6d - a - 4d = 12$
$\Rightarrow 2d = 12$
$\Rightarrow d = 6$
Putting the value of d in eq. $(i),$ we get
$a + 2 \times 6 = 16$
$\Rightarrow a = 4$
$\therefore A.P$. is $\{4, 10, 16, 22,\}$
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