Question

If d is the common difference of the AP whose Kth term is ak, then a k+1-ak is equal to

Answer 1

SOLUTION

GIVEN

d is the common difference of the AP whose Kth term is $\sf{a_k}$

TO DETERMINE

$\sf{a_{k + 1} - a_k}$

EVALUATION

Let x be the first term of the AP ( Arithmetic progression)

It is given that common difference = d

$\therefore \sf{ k \: th \: term \: = a_k }$

$\sf{= x + (k - 1)d}$

$= \sf{ x + kd -d}$

$\sf{ \therefore( k + 1)\: th \: term \: = a_{k + 1}}$

$\sf{ = x + (k + 1 - 1)d}$

$\sf{ = x + kd}$

Now

$\sf{a_{k + 1} - a_k}$

$= \sf{x + kd - (x + kd - d)}$

$= \sf{x + kd - x - kd + d}$

$= \sf{d}$

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