Question

The $6^{th}$ term of an arithmetic progression is $-10$ and the ${10}^{th}$ term is $-26.$ Determine the ${15}^{th}$ term of the AP.

• A. ${15}^{th}$ term of AP is $-14$
• B. ${15}^{th}$ term of AP is $-86$
• C. ${15}^{th}$ term of AP is $-46$
• D. ${15}^{th}$ term of AP is $-35$

Answer 1

Answer: (C)

${15}^{th}$ term of AP is $-46$

Let $a$ and $d$ be the first term and common difference of the given AP respectively.
$\therefore a_6=-10\Rightarrow a+5d=-10$ ...(1)
& $a_{10}=-26\Rightarrow a+9d=-26$ ...(2)
On subtracting (1) from (2), we get
$4d=-16\Rightarrow d=-4$
Putting $d=-4$ in (1), we get
$a=-10-(5\times -4)=10$
Now, $a_{15}=a+14d=10+14\times -4=-46$
Hence, ${15}^{th}$ term of the given AP is $-46$.