the sum of furst m terms of an A. P. us 4msquare-m if its nth term is 107 find the value of n. Also find 21st term
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Answer:
Sum of m term =S
m
=4m
2
−m
⇒mthterm=T
m
=S
m
−S
m−1
⇒Tm=(4m
2
−m)−(4(m−1)
2
−(m−1))
=(4m
2
−m)−(4(m
2
−2m+1)−(m−1))
=4m
2
−m−(4m
2
−8m+4−m+1)
=4m
2
−m−(4m
2
−9m+5)
=4m
2
−m−4m
2
+9m−5
=8m−5
⇒ntlTerm=T
n
=8n−5
As T
n
=107
⇒8n−5=107
⇒8n=107+5=112
⇒n=
8
112
=14
⇒14
th
term is 107
21
st
term is given by
T
21
=8(21)−5
=168−5=163
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