Question

sum of first n terms of an AP is 5n 2 -3n. find the AP and also find its 16th term.

Answer 1

question given
Sn=5n^2-3n

we know
tn=Sn-S(n-1)
where tn is nth term in AP and Sn is sum of n term and Sn (n-1) is sum of n-1 term
now
tn=5n^2-3n-5 (n-1)^2+3 (n-1)
=5n^2-3n-5n^2+10n-5+3n-3
=10n-8
hence tn=10n-8
t1=10 (1)-8=2
t2=10 (2)-8=12
t3=10 (3)-8=22
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hence AP is 2 ,12,22,32,.........
now
t16=10 (16)-8=152
hence 16th term of AP is 152