Question

If tn is the nth term of an ap then the value of tn+1-tn-1 is what? With detailed answer ​

Answer 1

Answer:

The answer is 2d

explanation is in picture

Answer 2

Given:

tn is the nth term of an AP.

To find:

The value of tn + 1 - tn - 1.

Solution:

The value of tn + 1 - tn - 1 is 2d.

To answer this question, we will follow the following steps:

As we know that the nth term of an AP is given by using the formula:

$a + (n - 1)d$

Where a = first term, d = common difference

Now,

As given in the question,

the nth term of an AP = tn

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

So,

$a + (n - 1)d = tn$

Now,

$t_{n + 1} = a + (n + 1 - 1)d$

$= a +(n - 1 + 1)d$

$= tn + d$

Also,

$t_{n - 1} = a + (n - 1 - 1)d$

$= a + (n - 1)d - d$

$= tn - d$

So,

$(t_{n + 1}) - (t_{n - 1}) = (tn + d) - (tn - d)$

On solving the above, we get

$= 2d$

Hence, the value of tn + 1 - tn - 1 is 2d.