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

Sagot :

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

[tex]\Rightarrow 7=a+d\quad \ldots(i)\\\Rightarrow 23=a+5d\quad \ldots(ii)[/tex]

Subtract the above equations

[tex]\Rightarrow 23-7=5d-d\\\Rightarrow 16=4d\\\Rightarrow d=4[/tex]

Put d in equation (i)

[tex]\Rightarrow 7=a+4\\\Rightarrow a=3[/tex]

So, the third term of the AP is [tex]a+2d[/tex]

[tex]\Rightarrow 3+2\times 4=11[/tex]

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