Question

Sum of first nth term of an arithematuc sequance is 3n2 =6n find its 15 th term

Answer 1

Answer:

sum of n terms is

$3 {n}^{2} = 6n \\ 3 {n}^{2} - 6n = 0$

15th term= sum of 15 terms - sum of 14 terms

$= 3 {(15)}^{2} - 6(15) - 3 {(14)}^{2} + 6(14) \\ = 3 {(15)}^{2} - 3 {(14)}^{2} - 6(15) + 6(14) \\ = 3(( {15)}^{2} - {(14)}^{2} ) + 6( - 15 + 14) \\ = 3((15 - 14)(15 + 14) + 6( - 1) \\ = 3 \times 1 \times 29 - 6 \\ = 87 - 6 \\ = 81$