Question

If 6th and 17th term of an A.P are 19 and 52 then what is the 10th term

Answer 1

$\sf{\large{\underline{\underline{EXPLANATION:}}}}$

$\sf{Given}\begin{cases}\sf{a_{6}=19}\\ \sf{a_{17}=52}\\ \sf{a_{10}=??}\end{cases}$

★We know,,

$\sf{a_{6}=a+5d}$

$\sf{\implies{19=a+5d}}$

$\sf{\implies{a=19-5d...(1)}}$

★And,,

$\sf{a_{17}=a+16d}$

$\sf{\implies{52=a+16d}}$

$\sf{\implies{a=52-16d...(2)}}$

★From eq(1) and (2),

$\sf{19-5d=52-16d}$

$\sf{\implies{16d-5d=52-19}}$

$\sf{\implies{11d=33}}$

$\sf{\implies{d=3}}$

★And,,

$\sf{a=19-5d}$

$\sf{\implies{a=15-(5×3)}}$

$\sf{\implies{a=15-15}}$

$\sf{\implies{a=0}}$

★Therefore,,

$\sf{a_{10}=a+9d}$

$\sf{\implies{a_{10}=0+(9×3)}}$

$\sf{\implies{\boxed{a_{10}=27}}}$

$\rule{200}2$

Hope it helps ❣️❣️❣️