Question

Find the rth term of an A.P., the sum of whose first `n` terms is `3n^2+4n`

Answer 1

`S_n=3n^2+4n`
`S_1=3*1^2+4*1`
`=7=a_1`
`S_2=3*2^2+4*2`
`=12+8=20`
`S_2-S_1=a_2`
`20-S_1=a_2`
`a_2=13`
`a_1=7`
`a_2=13`
`d=a_2-a_1=6`
`T_r=a_1+(r-1)d`
`=7+(r-1)6`
`=7+6r-6`
`=1+6r`.