Question

find tn if t3=22 and t17=-20

Answer 1

t3=22
or,a+2d=22......(i)
And,
t17= -20
or,a+16d= -20.....(ii)
Solving (i) and (ii)
a+2d=22
a+16d=-20
- - +
-14d =42
d = -3
Putting d=-3 in eqn (i)
a+2d =22
or,a+2×(-3)=22
or,a-6 =22
a =28
Now,
tn=a+(n-1)d
=28+(n-1)(-3)
=28-3n+3
= -3n+31

Answer 2

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As we know,
tn = a+(n-1)d
Now t3 = 22 and t17 = -20
so, t3 = a+(3-1)d
= a+2d ......eq(1)
similarly , t17 = a+16d ......eq(2)
Now solving eq(1) and eq (2) by elimination method...
we get d = -3 and a = 28
so tn = 28+(n-1)(-3)

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