Question

the 10th term of an A. P is -4 and it's 22nd term is -16. find its 38th term. also find its nth term​

Answer 1

Answer:

a + 9d = -4

a + 21d = -16

Subtracting both the equations...

we get, d = -1

Substituting the value of d in equation 1

we get, a - 9 = -4

a = 5

Therefore, 38th term = a + 37d

= 5 + 37(-1)

= 5 - 37 = -32

nth term = a + (n-1)d

= 5 + (n-1)-1

= 5 - n + 1

= 6 - n

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Answer 2

a10=-4

a+9d=-4 ----(1)

a22=-16

a+21d=-16---(2)

(1)-(2)

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

-12d=12

d=-1

(1)==>a=5

Therefore,

a38=a+37d

=5-37

=-32

Therefore,

an=a+(n-1)d

=5+(n-1)(-1)

=5-n+1

=6-n

Therefore the required 38th term and nth term are (-24) & (6-n)

Hope it will help you.