Question

What is the 14th term of an A.P whose 5th term is 11 and 9th term is 7​

Answer 1

Answer:

Here, we have to find 14th term.

Step-by-step explanation:

Here, 5th term is 11 =

.... a+4d = 11 →_→ (equation 1)

AND,

9th term =

a+8d = 7 (equation 2)

Equation (2)—Equation (1) =

a+8d—(a+4d) = 7—11

a+8d—a—4d = —4

4 d = —4

d = —4/4

d = —1

PUTTING THE VALUE OF D IN Equation (1).

a + 4d = 11

a +4×(—1) = 11

a +(—4) = 11

a = 11+4

a = 15

Thus, the first term of the A.P is 15 and the common difference of the A.P is (—1).

Formula to find the nth term of the A. P = a+(n—1)×d

Then, it's 14th term = a+(14—1)×d

= a + 13d [Equation 3]

PUTTING THE value of a and d in the Equation 3.

15+13×(—1)

= 15—13

= 2

Hence, the 14th term of the A. P. is 2.

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