Correct Answer - Option 4 : 0
Given:
15T21 = 20T31
Formula used:
Tn = a + (n – 1) d
Where, a = first term, n = the number of term and d = common difference
Calculation:
T21 = a + (21 – 1) d
⇒ T21 = a + 20d ----- (1)
T31 = a + (31 – 1) d
⇒ T31 = a + 30d ----- (2)
According to question –
⇒ 15 × (a + 20d) = 20 × (a + 30d)
⇒ 15a + 300d = 20a + 600d
⇒ 5a + 300d = 0
⇒ a + 60d = 0 ----- (3)
From equation (3), we have –
∴ T61 = a + (61 – 1) d
⇒ T61 = a + 60d = 0
∴ 61st term of the A.P. is zero.