Question

If twelfth term of an A.P is 30, then the sum of its fifth, twelfth and nineteenth term is

Answer 1

The formula for nth term is

T(n)=a+(n-1)d

12th Term of AP is 30

30=a+(12–1)d

30=a+11d—————Equation 1

now,

we need to find sum of its fifth, twelfth and nineteenth term

a5 + a12 + a19 = ?

so, let, a5 + a12 + a19 = X

X = a5 + a12 + a19

=> X = (a + 4d) + (a + 11d) + (a + 18d)

=> X = 3a + 33d

=> X = 3( a + 11 d)

(using equation 1 we get)

=> X = 3 × 30

=> X = 90

Therefore, the sum of its fifth, twelfth and nineteenth term is 90