Question

The 6th term of an A.P. is equal to 4 times its first term, and the sum of the first 6 terms is 75. Find the first term and the common difference.

Answer 1

T_n = a + (n − 1)d

T₆ = a + (6 − 1)d

T₆ = a + 5d = 4 × a

a + 5d = 4a

5d = 3a

`S_6 = 6/2[2a + (6 - 1)d]`

`S_6 = 3[2a + 5d] = 75`

3[2a + 3a] = 75

3 × 5a = 75

a = `75/15`

a = 5

5d = 3a

5d = 3 × 5

5d = 15

d = `15/5`

d = 3