Question

For some real number t, the first $3$ terms of an arithmetic sequence are $3t,4t+2$, and $7t-4$. What is the numerical value of the $4th$ term?

• A. $15$
• B. $16$
• C. $26$
• D. $30$

Answer 1

The correct option is D $30$

Common difference of an arithmetic sequence is constant
Difference between the first two terms is $(4t+2)-\left(3t\right)=t+2$
Difference between the 2nd and 3rd terms is $(7t-4)-(4t+2)=3t-6$

Therefore,
$t+2=3t-6$
$3t-t=2+6$

$2t=8$

$t=4$

And the common difference is $t+2=4+2=6$.

Hence, the sequence is $12,18,24,30,...$