Question

If the first and third of an arithmetic sequence 2 and 22 respectively whatis its second term?

Answer 1

       $\underline{\bold{Answer:}}$

       $12$

       $\underline{\bold{Step-by-step-explaination:}}$

       $\text{First term of A.P}(a_1) = 2$

       $\text{Third term of A.P}(a_3) = 22$

       $\text{Second term of A.P}(a_2) = \text{ ?}$

       $\text{We know that any term in an A.P, other than the first, is the arithmetic }\\\text{mean of the previous and the next term in the A.P}$

$\implies \boxed{a_2 = \frac{a_1 + a_3}{2} }$

$\implies \boxed{a_2 = \frac{2 + 22 }{2} }$

$\implies \boxed{a_2 = \frac{24}{2} }$

$\implies \boxed{a_2 = 12 }$

Answer 2

Answer:

1212

\underline{\bold{Step-by-step-explaination:}}

Step−by−step−explaination:

\text{First term of A.P}(a_1) = 2First term of A.P(a

1

)=2

\text{Third term of A.P}(a_3) = 22Third term of A.P(a

3

)=22

\text{Second term of A.P}(a_2) = \text{ ?}Second term of A.P(a

2

)= ?

\begin{gathered}\text{We know that any term in an A.P, other than the first, is the arithmetic }\\\text{mean of the previous and the next term in the A.P}\end{gathered}

We know that any term in an A.P, other than the first, is the arithmetic

mean of the previous and the next term in the A.P

\implies \boxed{a_2 = \frac{a_1 + a_3}{2} }⟹

a

2

=

2

a

1

+a

3

\implies \boxed{a_2 = \frac{2 + 22 }{2} }⟹

a

2

=

2

2+22

\implies \boxed{a_2 = \frac{24}{2} }⟹

a

2

=

2

24

\implies \boxed{a_2 = 12 }⟹

a

2

=12