Question

If 6 times the 6th term of an AP is equal to 15 times the 15th term, Find the 21st term

Answer 1

6th term

a6 = a + (6 - 1)d
a6 = a + 5d

15th term

a15 = a + (15 - 1)d
a15 = a + 14d

According to question,

6 (a6) = 15 (a15)
6 (a + 5d) = 15 (a + 14d)
6a + 30d = 15a + 210d
0 = 15a - 6a + 210d - 30d
0 = 9a + 180d
0 = 9(a + 20d)
0 = a + 20d
- 20d = a. ....(1)

21 term

a21 = a + (21 - 1)d
a21 = -20d + -21d. [from equation (1)]
a21 = 0

Answer. 21st term is 0.

Answer 2

Answer:

6(a+5d) =15(a+14d)

6a+30d=15a+210d

9a+180d

common 9

9(a+20d)

20d=a

a=-20d

a21=a+(20) d

a21=-20d+20d=0