Question

If 4 5 , a and 2 are three consecutive terms of an A. P. ,then find the value of a.

Answer 1

1st Term Is 4/5

2nd Term Is a

3rd term is 2

Now as these terms are consecutive

Second Term -first Term = Third Term - Second Term

As d=d

So,

a-4/5=2-a

5a-4/5=2-a

5a-4=5(2-a)

5a-4=10-5a

5a+5a=10+4

10a=14

a=14/10

a=7/5

Hence Value Of a is 7/5.

I hope it will help u Buddy.

Pls mark it as brainliest ans buddy.

Answer 2

Answer:

7/5

Step-by-step explanation:

Here, 4/5, 'a', 2,... are in AP.

The simplest method to find the value of 'a' is to divide the sum of the terms at left and right of 'a' by 2.

That is,

$a = \frac{\frac{4}{5} + 2}{2} = \frac{\frac{4}{5} + \frac{10}{5}}{2} = \frac{\frac{14}{5}}{2} \\ \\ \\ a = \frac{14}{5} \div 2 = \frac{14}{5} \times \frac{1}{2} = \frac{14}{10} = \bold{\frac{7}{5} = 1\frac{2}{5}}$

∴ 7/5 is the answer.

.....................................................................................................................................

How I made possible finding the answer quickly by this simple method???!!!

Okay, let me explain.

Let 4/5, a, 2,... are the first consecutive terms of an AP.

Let the first term 4/5 be f.

Let the common difference be d.

So,

4/5 = f

a = f + d

2 = f + 2d

The method I've done is going to be done algebraically as shown below.

In the method I preferred, at first, I added first and third terms, i.e., 4/5 and 2.

$\frac{4}{5} + 2 = \frac{14}{5} \\ \\ f+f+2d = \frac{14}{5} \\ \\ 2f+2d = \frac{14}{5} \\ \\ 2(f+d) = \frac{14}{5}$

Then I divided this sum by 2 to get the answer, i.e., the value of 'a'.

$\frac{2(f+d)}{2} = \frac{\frac{14}{5}}{2} = \frac{7}{5}\\ \\ f+d = \frac{7}{5}$

We got that f + d = 7/5. We considered earlier that, f + d = a.

Then how we can say that the value of a is none other than 7/5 ???!!!

Hope this may be helpful.

Thank you. Have a nice day. :-)

#adithyasajeevan