Question

The 6th term of an AP is -10 and 10th term is -26. Determine the 15th term of the AP

Answer 1

Solution is attached below

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 equations (i) and  (ii):-

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

-10 - 5d = -26 - 9d

9d - 5d = -26 + 10

4d = -16

d = -4

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 AP:-

Formula = a + (n-1)d

a + (n-1)d

10 + (15-1)(-4)

10 + 14(-4)

10 - 56

-46

Hope it helps

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