Question

The sixth term of an ap is-10 and 10th term is-26 determine the15th term of an ap

Answer 1

Given,
a6=-10
a10=-26.

As we know that,

An=a+(n-1)d
A6=a+(6-1)d
-10=a+5d
a+5d=-10---------------(1)

again,

An=a+(n-1)d
A10=a+(10+1)d
-26=a+9d
a+9d=-26------------(2)

Now ,equation (2)-(1)

a+9d=-26
a+5d=-10
(-) (-) (+)
________
4d=-16
d=-16/4
d=-4.

putting the value of d=-4in equation (1) we get,

a+5d=-10
a+5×(-4)=-10
a-20=-10
a=-10+20
a=10.

therefore,the 15th term is ,

An=a+(n-1)d
A15=10+(15+1)×(-4)
A15=10+14×(-4)
A15=10-56
A15=-46.

THEREFORE 15th term is -46.

HOPE IT HELPS you!!!!

Answer 2

Answer:

6th term of AP = -10

⇒ a + (n-1)d = -10

a + (6-1)d = -10

a + 5d = -10

a = -10 - 5d — (i)

10th term of AP = -26

⇒ a + (n-1)d = -26

a + (10-1)d = -26

a + 9d = -26

a = -26 - 9d — (ii)

Now we compare both the equations:-

Since we know that both the equations stand for the value of ‘a’, we can say that they are equal to each other.

-26 - 9d = -10 - 5d

-26 + 10 = -5d + 9d

-16 = 4d

-4 = d

Now we find the value of ‘a’ by substituting the value of ‘d’ in equation (i):-

a = -10 - 5d

a = -10 - 5(-4)

a = -10 + 20

a = 10

Now we find the 15th term of the AP:-

Formula = a + (n-1)d

⇒ 10 + (15-1)-4

10 + (14)-4

10 + (-56)

10 - 56

-46 Ans

15th term of AP = -46

Hope it helps

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