Question

The sum of first n terms of an ap is 3n2+2n find the ap an dits 19th term

Answer 1

Hope it helps you

Please mark this as brainliest.

Answer 2

   

$S_n=3n^2+2n \\ \\ \\ \Rightarrow\ S_1=3(1)^2+2(1) \\ \\ \Rightarrow\ a_1=3+2 \\ \\ \Rightarrow\ a_1=5 \\ \\ \\ \Rightarrow\ S_2=3(2)^2+2(2) \\ \\ \Rightarrow\ a_1+a_2=3 \times 4+4 \\ \\ \Rightarrow\ 5+a_2=12+4 \\ \\ \Rightarrow\ 5+a_2=16 \\ \\ \Rightarrow\ a_2=11 \\ \\ \\ \Rightarrow\ d=a_2-a_1 \\ \\ \Rightarrow\ d=11-5 \\ \\ \Rightarrow\ d=6$

So the AP is 5, 11, 17, 23...

$\Rightarrow\ a_{19}=a_1+18d \\ \\ \Rightarrow\ a_{19}=5+18 \times 6 \\ \\ \Rightarrow\ a_{19}=5+108 \\ \\ \Rightarrow\ a_{19}=\bold{113}$

So the 19th term is 113.

Thank you...