the sum of first 7 terms of an A.P.is 168 and the 11th term is 59.find the sum of its first 30terms.also find the 30th term.
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Step-by-step explanation:


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Class 11
>>Applied Mathematics
>>Sequences and series
>>Arithmetic progression
>>The sum of first n terms of an A.P is 5n
Question

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

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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
Answer:
tn=a+(n-1)d
t7=a+6d=168
t11=a+10d=59
solve linear equation you get a and d
then put a and d value in
t30=a+29d
you get answer