Question

If the 9th term of an A.p. is zero then show the 29th term is twice the 19th term​

Answer 1

If the 9th term of an AP is zero, then prove that its 29th term is twice its 19th term. Solution : Let the first term, common difference and number of terms of an AP are a, d and n, respectively. Hence, its 29th term is twice its 19th term.
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Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

If the 9th term of an A.P is 0 then show the 29th term is twice the 19th term.

$\underline{\bf{Explanation\::}}$

As we know that formula of the arithmetic progression;

$\boxed{\bf{a_n = a+(n-1)d}}$

• a is the first term
• d is the common difference
• n is the term of an A.P.

A/q

$\mapsto\tt{a_9 = 0}$

$\mapsto\tt{a+(9-1)d = 0}$

$\mapsto\tt{a+8d=0............(1)}$

&

$\mapsto\tt{a_{29}= 2 \times a_{19}}$

Taking L.H.S :

→ a+(29-1)d

→ a + 28d

→ a + 8d + 20d

→ 0 + 20d [from (1)]

→ 20d

Taking R.H.S :

→ 2 × [a + (19 - 1)d]

→ 2 × [a + 18d]

→ 2 × [a + 8d + 10d]

→ 2 × [0 + 10d]   [from(1)]

→ 2 × 10d

→ 20d

Thus,

L.H.S = R.H.S

Proved .