Question

if 3, k-2, 5 are three terms of an A.P then k equal to​

Answer 1

We know that :-

$\tt If \: three \: numbers \: a,b, c \: are \: in \: A.P \: then : \\ \\ \boxed{\boxed{\tt \large 2b = a + c}}$

$\tt \: here : \\ \\ \tt \rightarrow a = 3\\ \\ \tt \rightarrow b = k - 2\\ \\ \tt \rightarrow c = 5$

$\tt \longrightarrow 2(k - 2) = 3+ 5 \\ \\ \tt \longrightarrow 2k -4 =8 \\ \\ \tt \longrightarrow 2k= 8 + 4\\ \\ \tt \longrightarrow 2k=12\\ \\ \tt \longrightarrow k= 6$

Answer :

value of k = 6

$\tt \large \underline{Additional- Information }:$

$\boxed{ \boxed{\tt \large T_n = a+(n-1)d} } \\ \\ \tt where : \\ \\ \tt \bull T_n = n_{th} \: term \\ \\ \tt \bull n = number \: of \: terms \\ \\ \tt \bull a= first \: term \\ \\ \tt \bull d = common \: difference$