Question

if there are 15 terms in an AP whose first term is
$\sqrt{2}$
and the common difference is root 2root 2 ,then it's last term is
a) 31 root 2
b) 30 root 2
c) 29 root 2
d) 28 root 2​

Answer 1

Given: There are 15 terms in an AP whose first term is ✓2 and the common difference is 2✓2.

To find: The last term of the AP

Explanation: Let the first term be denoted by a and the common difference be denoted by d.

a= ✓2

d = 2✓2

Any nth term of an AP is given by the formula:

a + (n-1)d

There are 15 terms in this AP. So the last term is the 15th term of the AP.

Using the formula given above:

Last term= a + (15-1) d

= ✓2 + 14 (2✓2)

= ✓2 + 28✓2

= 29✓2

Therefore, the last term of the AP is option (c) 29✓2.

Answer 2

Given:

There are 15 terms in an AP.

First term, a = √2

Common difference, d = 2√2

To find :

The last term in AP.

Formula to be used:

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

Solution:

There are 15 terms in an AP.Then, the last term is 15.

We can find the 15th term by using the following formula,

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

n = 15 , a = √2 ,  d = 2√2

$t_{15} = \sqrt{2} + (15-1)2\sqrt{2}$

$t_{15} = \sqrt{2} + 30\sqrt{2} -2\sqrt{2}$

$t_{15} =31\sqrt{2} -2\sqrt{2}$

$t_{15} =29 \sqrt{2}$

The 15th term in AP is $29\sqrt{2}$

Final answer:

The last term in AP is $29\sqrt{2}$

Thus, the correct option is c) 29 root 2