Question

10 the sum of the 15 and 17" terms of an arithmetic sequence is 40. The sum of its 1" and
18 terms is 43.
a) What is its common difference?
b) What is the sum of its 7" and 11 terms?
B
c) Find its 9 term.
D​

Answer 1

Correct Question:-

The sum of the 1st and 17th terms of an arithmetic sequence is 40. The sum of its 1st and 18th terms is 43.

a) What is the common difference?

b) What is the sum of 7th and 11th terms?

c) Find its 9th term.

Answer:-

Given:

Sum of 1st and 17th term of an AP = 40

Sum of 1st and 18th terms = 43

We know that,

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

Hence,

→ a + a + (17 - 1)d = 40

→ 2a + 16d = 40 -- equation (1)

Similarly,

→ a + a + (18 - 1)d = 43

→ 2a + 17d = 43 -- equation (2)

Subtract equation (1) from (2).

→ 2a + 17d - (2a + 16d) = 43 - 40

→ 2a + 17d - 2a - 16d = 3

→ d = 3

Substitute d value in equation (1).

→ 2a + 16(3) = 40

→ 2a = 40 - 48

→ 2a = - 8

→ a = - 8/2

→ a = - 4

Now,

a(7) = - 4 + (7 - 1)(3)

→ a(7) = - 4 + 18

→ a(7) = 14

a(11) = - 4 + (11 - 1)(3)

→ a(11) = - 4 + 30

→ a(11) = 26

Sum of 7th term and 11th term = 14 + 26 = 40.

• a(9) = - 4 + (9 - 1)(3)

→ a(9) = - 4 + 24

→ a(9) = 20

Therefore,

• Common difference = 3.

• Sum of its 7th & 11th terms = 40.

• 9th term is 20.