Question

Two aps have the same common difference. the first term of one of these is–1 and that of the other is – 8. then the difference between their 4th terms is

Answer 1

$let \: common \: difference \: of \: both \: the \: aps \: be \: d \\ and \: let \: their \: nth \: term \: be \: a_{n} \: and \: b_{n} \: respectively \\ \: a_{n} = (n - 1)d - 1 \: and \:b_{n} = (n - 1)d - 8 \\ now \: \: a_{n} - b_{n} = (n - 1)d - 1 - (n - 1)d + 8 \\ a_{n} - b_{n} = 7 \\ a_{4} - b_{4} = 7 \\ hence \: 7 \: is \: the \: answer$