Question

in an AP the sum of first n terms is 5n^2/2+3n/2. find its 20th term

Answer 1

given sum Tn= 5n^2 / 2 + 3n / 2 ----(1)

let ,n= 1,2,3..

put n = 1 in eq(1)

T1= 5(1)^2 / 2 + 3(1) / 2

T1= 5/ 2 + 3 / 2 = 8 / 2 = 4

T1 =4
first term T1 = 4
now put ,n = 2 in (1),we get,

T2 = 5(2)^2 / 2 + 3(2) / 2

T2 = 20 / 2 + 6 / 2

T2 = 13

now put n = 3 in (1), we get

T3 = 45 / 2+ 9 / 2

T3= 27

common difference (d) = (T3 - T2) - ( T2 - T1)
d = (27 - 13) - ( 13 - 4)

d = 14 - 9 = 5

d = 5, and T1= 4 = a

so now, T20 = a+ 19d

T20 = 4 + 19 ( 5)

T20= 4+ 95 = 99

T20 = 99


hence ,the 20th term = 99

★hope it helps ★