Question

If 15th term of AP is 0 and 4th term is 12 .find 12th term

Answer 1

ANSWER:

Given

• 15th term ( t15 ) = 0
• 4th term ( t4 ) = 12

TO FIND:

The 12th term of A.P.

Using

tn = a + (n - 1)d

Similarly

⇒t15 = a + (14 - 1)d = a + 14d = 0 _______( 1 )

⇒t4 = a + (4 - 1)d = a + 3d = 12_________( 2 )

Equation ( 2 ) - ( 1 )

${ \sf{ \: \: \: \: \: t_{4} = \cancel{a} + 3d = 12 }} \\ { \sf{ \: \: \: \: t_{12} = \cancel{a} + 14d = 0}} \\ \small{ \underline{ ( - ) \: \: \: \: \: \: \: ( - ) \: \: \: ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \to { \sf{ \: \: - \: 11d = 12 }} \\ { \sf{ \to \:common \: difference(d) = \frac{12}{ - 11} = - \frac{12}{11} }}$

Substituting d = - 11/12 in equation 1

t15 = a + 14(-11/12)

t15 = a - 77/6

0 = a -77/6

77/6 = a

First term ( a ) = 77/6

We need to find 12th term of A.P

t12 = a + (12 - 1)d = a + 11d

Substituting the values of a & d

→ t12 = 77/6 + 11(-11/12)

→ t12 = 77/6 - 121/12

→ t12 = 154 - 121/12

→ t12 = 33/12

Hence, 12th term(t12) = 33/12