MAHARASHTRA Class 10: General Term of an A.P. Videos | Calculating nth term in an Arithmetic progression

In the given AP, there are 51 terms and the first term a = 4. 

d = a₂− a₁ = 9 − 4 = 5

The 8^th term from the end of an AP will be the 44^th term. 

According to the formula,

∴ a₄₄ =a + (44 − 1)d = 4 + 43 × 5 = 219 

a = 3

d = 10 − 3 = 7

According to the formula,

a_n = a + (n − 1)d

∴ a₁₃ =3 + (13 − 1)7= 3 + 12 × 7 = 87

87 + 84 = 171

According to the formula,

a_n = a + (n − 1)d

171 = 3 + (n − 1)7

∴171 = 3 + 7n − 7

∴7n = 175

∴n = 25 

According to the formula,

a_n = a + (n − 1)d

a₈ =a + (8 − 1)d = a + 7d = 60 …(1)

a₁₂ =a + (12 − 1)d= a + 11d = 48 …(2)

Subtracting (2) from (1), we get

∴12 = −4d

∴ d = −3