Question

What is the third term of an arithmetic sequence whose second term is 7 and whose sixth term is 23​

Answer 1

Answer: 11

Step-by-step explanation:

Given

The second term of an AP is 7

The sixth term of an AP is 23

Suppose a and d be the first term and common difference of the sequence

$\Rightarrow 7=a+d\quad \ldots(i)\\\Rightarrow 23=a+5d\quad \ldots(ii)$

Subtract the above equations

$\Rightarrow 23-7=5d-d\\\Rightarrow 16=4d\\\Rightarrow d=4$

Put d in equation (i)

$\Rightarrow 7=a+4\\\Rightarrow a=3$

So, the third term of the AP is $a+2d$

$\Rightarrow 3+2\times 4=11$