Question

Can anyone answer the 10th question?

Answer 1

Hey There,


Let The AP be a, a+d, a+2d, ....



Then the $n^{th}$ term is given by:

$T_n=a+(n-1)d$

Thus, we have the following data:

$T_m=a+(m-1)d \\ \\ T_{m+n}=a+(m+n-1)d \\ \\ T_{m-n}=a+(m-n-1)d$

Now, we can go to your question:

$LHS \\ \\ = T_{m+n}+T_{m-n} \\ \\ = a+(m+n-1)d + a+(m-n-1)d \\ \\ =2a + (m+n-1+m-n-1)d \\ \\ = 2a + (2m-2)d \\ \\ = 2(a+(m-1)d) \\ \\ = 2T_m \\ \\ =\,\,RHS$

Hope it helps
Purva
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