Question

in a ap the sum of first n terms is (3n²/2+13n/2) find the 25th term

Answer 1

please find the attachment

Answer 2

${S}_{n} = \frac {{3}_{n}²+{13}_{n}}{2} \\\\\ {a}_{n} = {S}_{n}-{S}_{n-1} \\\\\ {a}_{25} = {S}_{25}-{S}_{24} \\\\\ {a}_{25} = \frac {3(25)²+13(25)}{2} - \frac {3(24)²+13(24)}{2} \\\\\ {a}_{25} = \frac {1}{2} [3(25²-24²)+13(25-24)] \\\\\ {a}_{25} = \frac {1}{2} [3(49)+13] \\\\\ {a}_{25} = 80$