Question

if 12th term of an AP is 82 and 18th term is 124 then find out 24th term​

Answer 1

GIVEN:

The 12th term of an AP = a12 = 82

The 18th term of an AP = a18 = 124

TO FIND:

The 24th term of an AP

SOLUTION:

12th term:

a + 11d = 82 ---(1)

18th term:

a + 17d = 124 ----(2)

After subtracting both eq - (1) & (2), we get:

-6d = -42

d = 42/6

d = 7

Common Difference = 7

Substitute common difference (d) in eq - (1)

=> a + 11(7) = 82

=> a + 77 = 82

=> a = 82 - 77

=> a = 5

First term = 5

Now,

24th term = a + 23d

= 5 + 23(7)

= 5 + 161

= 166

Therefore, the 24th term is 166.

Answer 2

Answer :

24th term of the given sequence is 166.

Explanation :

Given ,

12th term of an AP is 82

=> t 12 = 82

18th term of an AP = 124

=> t 18 = 124

we know that,

tn = a + (n-1)d

• where a is first term.
• n is the number of the term.
• d is the common difference.

Now, by using this formula we can write ,

t (12) = a + (12-1)d

t (12) = a + 11d.

=> a + 11d = 82 -------(1)

t (18) = a + (18-1)d

t (18) = a + 17d

=> a + 17d = 124 ------(2)

Multiply eq(2) with (-1)

then we get,

- a - 17d = - 124

now, by solving both the equations we get,

a - a + (11d - 17d) = (82 - 124)

-6d = -42

d = 42/6

d = 7.

by, placing the value of d in the given Equation , we get,

a + 11(7) = 82

a + 77 = 82

a = 82 - 77

a = 5.

Now , we need to find the value of t(24)

t (24) = a + (24 - 1)d

t (24) = a + 23d

t (24) = 5 + (23 × 7)

t (24) = 5 + 161

t (24) = 166.

therefore, the value of the term t(24) is 166