Question

If the 3rd term of a G.P is 450 and 7th term is 36450 then determine the 10th term and nth term

Answer 1

As per the question.
T3=450
a+(n-1)d=450
a+(3-1)d=450
a+2d=450.......eq(1)
T7=36450
a+(n-1)d=36450
a+(7-1)d=36450
a+6d=36450...... eq(2) the
Now, multiply with eq 1 by 3 and eq 2 by 1, we get
3a+6d=1350.....(3)
a+6d=36450..... give as eq (4)
Subtracting eq (3) &(4).
3a+6d=1350
a+6d=36450
(-) (-). (-)
2a= -35100
a=-17550
Now putting the value of "a" in eq (1), we get
a+2d=450
-17550+2d=450
2d=450+17550
2d=18000
d=9000
Now, we fine T10& TN
T10=a+(n-1)d

-17550+(10-1)9000
=-17550+(9x9000)
=-17550+18000
=450
TN=a+(n-1)d
=-17550+(n-1)9000
=-17550+9000n-9000
=9000n-26550. ans
hope this will help you