Question

the sum of first n terms of an ap is given by sn=3nsquare-n determine the ap and its 25 term​

Answer 1

⋆ $\sf\ S_{n} = 3n^2 - n$

AnswEr :

${\bigstar\:\sf{S_{1} :}} \\\\\sf\longrightarrow\ S_{1} = 3(1)^2 - 1 \\\\\\\sf\longrightarrow\ S_{1} = 3 - 1 \\\\\\\longrightarrow\boxed{\bf\ S_{1} = 2} \\\\\\{\bigstar\:\sf{a_{1} :}} \\\\\sf\longrightarrow\ a_{1} = S_{1}$ \\\\\\

$\longrightarrow\boxed{\bf\ a_{1} = 2} \\\\{\bigstar\:\sf{S_{2} :}} \\\\\\sf\longrightarrow\ S_{2} = 3(2)^2 - 2\\\\\\\sf\longrightarrow\ S_{2} = 3(4) - 2\\\\\\\sf\longrightarrow\ S_{2} = 12 - 2\\\\\\\longrightarrow\boxed{S_{2}= 10}\\\\ {\bigstar\:\sf{a_{2} :}} \\\\\\\sf\longrightarrow\ a_{2} = S_{2} - S_{1} \\\\\\\sf\longrightarrow\a_{2} = 10 - 2 \\\\\longrightarrow\boxed{\bf\ a_{2} = 8}$