Question

Mark the correct alternative in each of the following:

If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
(a) 87
(b) 88
(c) 89
(d) 90

Answer 1

Answer: Option - C [ 89 ]

EXPLANATION:

GIVEN :

The 7th term of an AP = 34

a + 6d = 34 ------(1)

The thirteenth term = 64

a + 12d = 64 -----(2)

Solve eq - (1) and (2) to find the common difference (d).

a + 6d = 34

a + 12d = 64

(-)

------------------

-6d = -30

=> d = 30/6

=> d = 5

Common Difference (d) = 5

Substitute d in any equation to find the first term of AP (a)

a + 6(5) = 34

a + 30 = 34

a = 34 - 30

=> a = 4

First-term = 4

18th term :

a18 = a + 17d

= (4) + 17(5)

= 4 + 85

= 89

Therefore, the 18th term is 89.

Answer 2

Let,

• 'a' be the first term of A.P .

• 'd' be the common difference of A.P .

☮︎ According to the question,

Case - 1 ;-

⭐ 7th term of an A.P is 34 .

→ a + (7 - 1) d = 34

→ a + 6d = 34 ----(1)

Case - 2 ;-

⭐ 13th term of the A.P is 64 .

→ a + (13 - 1) d = 64

→ a + 12d = 64 ----(2)

♪ Substracting equation 1 from equation2, we get

➪ a + 12d - a - 6d = 64 - 34

➪ 6d = 30

➪ d = 30/6

➪ d = 5

♪ Putting the value of d in equation 1, we get

→ a + 6 × 5 = 34

→ a = 34 - 30

→ a = 4

☯︎ Hence the 18th term of the A.P is,

→ a + (18 - 1) d

→ 4 + 17 × 5

→ 4 + 85

→ 89

∴ The 18th term of A.P is '89' .