Question

the sum of first n term of an ap is 5n^2 +3m if its nth term is 168 find the value of m also find the 20th term of this AP

Answer 1

Answer:

Step-by-step explanation:

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

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