Question

.in an A.P the sum of first n term is 5n²÷2+3n÷2 find the 17th term​

Answer 1

Answer:

Sum of first n terms=

=5n²+3n

Putting n=1, S₁=t₁=5+3=8

Putting n=2, S₂=52²+32=20+6=26

∴, t₂=S₂-S₁=26-8=18

Putting n=3, S³=53²+33=45+9=54

∴, t₃=S₃-S₂=54-26=28

∴, First term=a=8,

common difference=28-18=18-8=10

∴, the mth term=

=8+(m-1)10=168

or, (m-1)10=168-8

or, m-1=160/10

or, m-1=16

or, m=16+1

or, m=17

∴, the 20th term =

=8+(20-1)10

=8+19×10

=8+190

=198

∴, m=17 and =198