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# The $n^{th}$ term of a progression is $2n+3$. What is the type of progression and what is its $15^{th}$ term.

$\begin{array}{1 1} GP,30 \\ AP,15 \\ GP,15 \\ AP,33 \end{array}$

Explanation : $T_{n}=2n+3$
$T_{n-1}=2(n-1)+3=2n-2+3$
$d=T_{n}-T_{n-1}=2n+3-2n-1=2$
$Since\;d\;is\;not\;a\;function\;of\;n\;and\;it\;is\;a\;constant\;,it\;is\;AP.$
$15^{th}\;term\;T_{15}=2*15+3=33.$