Question

If the last term of an A.P. is $118$ and the $8^{th}$ term from the end is $90$, then the common difference of the $A.P$. is

• A. $2$
• B. $4$
• C. $3$
• D. $-3$

Answer 1

The correct option is B $4$

Let a,d,n be the first term, common difference, and number of terms of the given AP respectively.
Given, last term $=a_n=118$
$\Rightarrow a+(n-1)d=118$ ...(1)
Again, $8th$ term from end=$(n-8+1)th$ term from beginning.
i.e.$8th$ term from end=$(n-7)th$ term from beginning $=90$
$\Rightarrow a_{n-7}=90$
$\Rightarrow a+(n-8)d=90$ ...(2)
Subtracting (2) from (1), we get
$7d=28\Rightarrow d=4$
Hence, option B is correct.