Question

The 10th term of an AP is (-4) and its 22nd term is (-16).find its 38th term

Answer 1

a+9d=-4
a+21d=-16
- - +
----------------

Answer 2

10th term =a+(n-1)d
-4=a+9d ------(i)
22nd term =a+(n-1)d
-16=a+21d------(II)

Now on subtracting i from Ii equation, we get
-16+4=a+21d-a-9d
-12=12d
d=-1
now on
putting d =-1 in equation first
-4=a-9
a=5
therefore
38th term =a+37d
=5-37=-32
therefore 38th term is -32.
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