If sum of 3rd & terms & an A. P. 7 then find the 10th term
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nth term t
n
=a+(n−1)d
a= First term
d= Common difference
n= number of terms
t
n
=n
th
term
a
3
+a
8
=7
a+2d+a+7d=7
2a+9d=7⟶(i) a
7
+a
14
=−3
a+6d+a+13d=−3
2a+19d=−3⟶(ii)
From (i) & (ii)
2a+9d=7
2a+19d=−3
−10d=10
d=−1,
a=8.
a
10
=a+9d=8+9(−1)=−1
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