Question

if d is common difference of an ap whose kth term is ak then ak+1-ak is equal to. (a) 2d, (b) d, (c) 2 (d) 1​

Answer 1

$\textbf{Given:}$

$\textsf{d is the common difference of an A.P whose k th term is}\;\mathsf{a_k}$

$\textbf{To find:}$

$\textsf{The value of}\;\mathsf{a_{k+1}-a_k}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{7cm} \\\textsf{The n th term of the A.P a, a+d, a+2d.........}\\\\\mathsf{t_n=a+(n-1)d}\\ \end{minipage}}$

$\textsf{Let a be the first term of the A.P}$

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

$\mathsf{=(a+(k+1-1)d)-(a+(k-1)d)}$

$\mathsf{=a+kd-(a+kd-d)}$

$\mathsf{=a+kd-a-kd+d)}$

$\mathsf{=d}$

$\implies\boxed{\mathsf{a_{k+1}-a_k}=d}$

$\therefore\textsf{Option (b) is correct}$

$\textbf{Find more:}$

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