Question

$a,2a-1,3a-2,4a-3,...$
For a particular number $a$, the first term in the sequence above is equal to $a$ and each term thereafter is $7$ greater than the previous term. What is the value of the $16th$ term in the sequence?

• A. $113$
• B. $110$
• C. $96$
• D. $120$
• E. $130$

Answer 1

The correct option is A $113$

As given, sequence is $a,2a-1,3a-\mathrm{2.....}$
The first term $\left(a\right)$ $=a$
The difference between two consecutive term $\left(d\right)$ $=7$
As the first term in the sequence above is equal to $a$ and each term there after is $7$ greater than the first term.
i.e: $(2a-1)-a=7$ ; a$=8$
Applying Arithmetic Progression formula for $n^{th}$ term,
$A_n=a+(n-1)d$$A_{16}=8+(16-1)7$
$A_{16}=8+105=113$
Hence, option A is correct.