Question

in an ap if the second and the third terms are 14 and 18 respectively find the 25th term​

Answer 1

Answer:

t25 = 106

Step-by-step explanation:

d = t3-t2 = 18-14 = 4

t2 = 14.

a+d = 14

a+4 = 14

a = 10

t25 = a+24d = 10+24(4) = 10+96 = 106

Answer 2

Solution!!

The concept of arithmetic progression has to be used here. The second and third term are given in the question. We have to find the twenty fifth term.

T₂ = 14

T₂ = 14T₃ = 18

T₂ = a + d

T₃ = a + 2d

14 = a + d...(1)

14 = a + d...(1)18 = a + 2d...(2)

Subtracting (1) and (2), we get,

14 - 18 = a - a + d - 2d

-4 = -d

d = 4

Putting the value of d in (1),

14 = a + d

14 = a + 4

a = 14 - 4

a = 10

Tₙ = a + (n - 1)d

T₂₅ = 10 + (25 - 1)4

T₂₅ = 10 + (24)4

T₂₅ = 10 + 96

T₂₅ = 106

Hence, the 25th term of the AP is 106.

Here,

a → First term

d → Difference between the terms