Question

In an Ap, the ratio of the 2nd term to the 6th term is 2/5.if the 8th term is 26, what is the 10th term?

Answer 1

Answer:

The answer to this question is: 32

Step-by-step explanation:

So, as you might already know

The 2nd and the 6th terms are (a + d) and (a + 5d) respectively.

The ratio of these terms is given to be 2/5.

Solving this ratio, we get;

a + d/a + 5d = 2/5

5(a + d) = 2(a + 5d)

5a + 5d = 2a + 10d

5a - 2a = 10d - 5d

3a = 5d

The 8th term is (a + 7d) = 26.

Substituting for a, we get a = 5 and d = 3.

Therefore, the 10th term is (a + 9d) = 32

Answer 2

Answer:

10th term is 32.

Step-by-step explanation:

Let a be the first term and d be the common difference of AP.

Then, according to formula

          nth term = a + (n-1)d

          2nd term = a + d

          6th term = a + 5d

Now, given that

          $\frac{a + d}{a + 5d} = \frac{2}{5}$

          $5(a + d ) = 2(a + 5d)\\5a + 5d = 2a + 10d\\3a = 5d$

and, 8th term = 26

        a + 7d = 26

Substituting for a, we get

d = 3 and a = 5

Now, 10th term = a + 9d

                          = 5 + 9*3

                          = 5 + 27

                          = 32