 Hello and welcome to the session. In this session we discuss the following question which says if Sn the sum of first m terms of an AP is given by Sn equal to 3n square minus 4n then find its nth term. Now if we have an with the nth term of an AP and Sn is the sum of first n terms of an AP and Sn minus 1 is the sum of minus 1 terms of an AP then we have the nth term that is an is equal to Sn minus Sn minus 1. This is the key idea that we use for this question. Let's proceed with the solution now. In the question we have that the sum of first n terms of an AP is given by Sn equal to 3n square minus 4n. Now let's find out Sn minus 1 that is in place of n we put n minus 1 so we have 3 into n minus 1 the whole square minus 4 into n minus 1 so this is equal to 3 into n square minus 2n plus 1 minus 4n plus 4 further we get this is equal to 3n square minus 6n plus 3 minus 4n plus 4 so further we get 3n square minus 10n plus 7 this is Sn minus 1. So if we take an to be the nth term of an AP so this nth term is equal to Sn minus Sn minus 1 this means we have an is equal to 3n square minus 4n minus 3n square minus 10n plus 7 the whole and so further we get an is equal to 3n square minus 4n minus 3n square plus 10n minus 7 3n square minus 3n square cancels then 10n minus 4n would be 6n so we have an is equal to 6n minus 7 thus we get the nth term of the AP is given by 6n minus 7 this is our final answer this completes the session hope you understood the solution of this question