Question

if 5 times the 5th term of an AP is equal to 10 times the 10th term show that its 15th term is zero

Answer 1

We know the formula for finding the nth term i.e. a+(n-1)d.
Now, As per the question,
5{a+(5-1)d} = 10{a+(10-1)d}
5{a+4d} = 10{a+9d}
5a+20d = 10a +90d
-5a = 70d
a= -14d.
a+14d = 0
a+ (15-1)d = 0, which is 15th term.

Read more on Brainly.in - https://brainly.in/question/1671215#readmore

Answer 2

Given:

5 times the 5th term of an AP is equal to 10 times the 10th term.

To find:

The 15th term is zero.

Solution:

As we know that in an A.P. having a = first term, d = common difference, the nth term is given by using the formula:

${n}^{th} \: term = a + (n - 1)d$

Now,

The 5th term of the A.P.

$= a + (5 - 1)d$

$= a + 4d$

Similarly,

The 10th term of the A.P.

$= a + 9d$

Now,

according to the question,

5 × 5th term of the A.P. = 10 × 10th term of the A.P.

So,

$5 \times (a + 4d) = 10 \times (a + 9d)$

On solving the above, we get

$a + 4d = 2 \times (a + 9d)$

$a + 4d = 2a + 18d$

$a = - 14d$

$a + 14d = 0 \: \: (i)$

Also,

The 15th term of the A.P.

$= a + (15 - 1)d$

$= a + 14d$

$= 0$

....from (i)

Hence proved that the 15th term of the A.P. is zero.