Question

The sum of first n terms of an A.P. is $5n^2$+3n. If its mth term is 168, find the value of m. Also, find the 20th terms of this A.P.

Answer 1

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, $S_3$=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