Question

Let an be the arithmetic progression, for which third term is 13 and eleventh term is 25. Find seventh term.

Answer 1

Answer:

19

Step-by-step explanation:

Given ,

Third term of an A.P(a₃) = 13

Eleventh term of an A.P(a₁₁) = 25

To Find :-

seventh term of an A.P(a₇)

How To Do :-

As they gave the value of 3rd term and 11th term of an A.P we need to find the value of first term (a) and common difference(d) from those two equations and we need to find the seventh term of an A.P.

Formula Required :-

General term of an A.P :-

aₙ = a + (n - 1)d

Solution :-

a₃ = 13

a + (3 - 1)d = 13

a + (2)d = 13

a + 2d = 13

[Let it be equation - 1]

a₁₁ = 25

a + (11 - 1)d = 25

a + (10)d = 25

a + 10d = 25

[Let ie be equation - 2]

Subtracting equation 1 from equation 2 :-

a + 10d - (a + 2d) = 25 - 13

a + 10d - a - 2d = 12

8d = 12

d = 12/8

d = 3/2

∴ Common difference = d = 3/2

Substituting value of 'd' in equation 1 :-

a + 2(3/2) = 13

a + 3 = 13

a = 13 - 3

a = 10

∴ First term = a = 10.

a₇ = a + (7 - 1)d

= a + 6d

= 10 + 6(3/2)

= 10 + 3(3)

= 10 + 9

= 19

∴ Seventh term of an A.P = 19