Question

Find the value of t7 + t9 for the next arithmetic progression 2, 4, 6 ....​

Answer 1

Answer

$32$ is the required answer.

Reason

The nth term of the A.P is $2n$.

Hence, $t_7=14$ and $t_9=18$, so the required answer is $32$.

Alternative Method

Since $\dfrac{t_7+t_9}{2} =t_8$, the answer is the value of $2 t_8$.

It is two times the 8th term, which is equal to $32$.

Learn more

Any number obtained by mean value is the middle term of the two values. The series and the mean is related to each other.

• A.M and A.P relation

$\dfrac{a+c}{2} = b \Longleftrightarrow a, b, c \text{ (A.P)}$

• G.M and G.P relation

$b^2=ac \Longleftrightarrow b=\pm \sqrt{ac} \Longleftrightarrow a, b, c \text{ (G.P)}$

• H.M and H.P relation*

$\dfrac{1}{a} +\dfrac{1}{c} =\dfrac{2}{b} \Longleftrightarrow b=\dfrac{2ac}{a+c} \Longleftrightarrow a, b, c \text{ (H.P)}$

*$a$, $b$, $c$ are in H.P then $\dfrac{1}{a}$, $\dfrac{1}{b}$, $\dfrac{1}{c}$ are in A.P.

Answer 2

I hope it helps all.

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