Question

If the 2nd term and 4nd term of A.P is 12 and 20 respectivily find the 25th term of that A.P

Answer 1

Answer:-

Given:

2nd term of an AP = 12

4th term = 20

We know that,

nth term of an AP = a + (n - 1)d

Hence,

a + (2 - 1)d = 12

→ a + d = 12 -- equation (1)

Similarly,

a + (4 - 1)d = 20

→ a + 3d = 20 -- equation (2)

Subtracting equation (1) from (2) we get,

→ a + 3d - (a + d) = 20 - 12

→ a + 3d - a - d = 8

→ 2d = 8

→ d = 8/2

→ d = 4

Substitute the value of "d" in equation (1).

→ a + d = 12

→ a + 4 = 12

→ a = 12 - 4

→ a = 8

Hence,

→ a(25) = 8 + (25 - 1)(4)

→ a(25) = 8 + 24*4

→ a(25) = 104

Therefore, the 25th term of the given AP is 104.

Answer 2

Given ,

The 2nd term and 4nd term of A.P is 12 and 20 respectivily

We know that , the nth term of an AP is given by

$\boxed{ \sf{a_{n} = a + (n - 1)d}}$

Thus ,

a + d = 12 --- (i)

a + 3d = 20 --- (ii)

Subtract eq (i) from eq (ii) , we get

3d - d = 20 - 12

2d = 8

d = 8/2

d = 4

Put d = 4 in eq (i) , we get

a + 4 = 12

a = 8

Therefore , The first term and common difference of AP is 8 and 4

$\therefore$ The 25th term of AP will be

25th term = 8 + (25 - 1)4

25th term = 8 + 24 × 4

25th term = 8 + 96

25th term = 104