Question

The sum of first n terms of an AP is 5n2 + 3n. If the mth term is 168 , find the value of m. Also fnd the 20th term of this AP

Answer 1

Sum of first n terms=$S_{n}$
=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=$t_{m}$
=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 =$t_{20}$
=8+(20-1)10
=8+19×10
=8+190
=198
∴, m=17 and $t_{20}$=198

Answer 2

Answer:

Sum of first n terms=S_{n}S

n

=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=t_{m}t

m

=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 =t_{20}t

20

=8+(20-1)10

=8+19×10

=8+190

=198

∴, m=17 and t_{20}t

20

=198