the sum of all terms of AP having 10 terms except for the first term is 99 and except for sixth term is 89. find the 8th term if the sum of the first and fifth term is equal to 10
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Given:
S
10
=99+T
1
..........(i)
S
10
=89+T
6
..........(ii)
where S
10
is the sum of 10 terms of the A.P. and T
1
,T
6
are the first and sixth term respectively.
Say a and d are the first term and common difference of the A.P. respectively.
∴S
10
=5{2a+9d};T
1
=a;T
6
=a+5d........(iii)
∴5{2a+9d}=a+99........(iv)
5{2a+9d}=a+89+5d........(v)
Subtracting (iv) and (v), we get,
10−5d=0
=>d=2........(vi)
Also given that
T
1
+T
5
=10
=>a+a+4d=10
=>2a+4×2=10
=>2a=2
=>a=1
∴T
3
=a+2d=1+2×2=5
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