Q5 of 202 Page 10

Write 5th term from the end of the A.P. 3, 5, 7, 9, ...., 201.

Here a = 201, a₂ = 5, a₃ = 7

d = a₃ – a₂ = a₂ – a₁

= 7 – 5 = 5 – 3 = 2

t_n = a + (n –1)d

t_n = 3 + (n–1)2 = 201

(n –1) 2 = 201 – 3 = 198

n – 1 = = 99

n= 99 + 1 =100

5^th term from end = 96th term

T₉₅ = 3 + (96 –1)2

T₉₅ = 3 + 95 x 2

T₉₅ = 3 + 190 = 193

Which tem of the sequence 114, 109, 104, .... is the first negative term?

Write the value of a₃₀ – a₁₀ for the A.P. 4, 9, 14, 19, ……….

Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.

Write the nth term of an A.P. the sum of whose n terms is S_n.