The ninth term of an AP is equal to seven times the

second term and twelfth term exceeds five times the

th

2 thoughts on “The ninth term of an AP is equal to seven times the <br /><br />second term and twelfth term exceeds five times the <br /><br />th”

1. Answer:

   Let the first term of AP be a and common difference be d.

   a9 = 7a2

   ⇒ a + 8d = 7(a + d) …(i)

   a12 = 5a3 + 2

   ⇒ a + 11d = 5(a + 2d) + 2 …(ii)

   From (i),

   a + 8d = 7a + 7d

   – 6a + d = 0 …(iii)

   From (ii),

   a + 11d = 5a + 10d + 2

   – 4a + d = 2 …(iv)

   Subtracting (iv) from (iii),

   – 2a = – 2

   ⇒ a = 1

   From (iii),

   – 6 + d = 0

   d = 6

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2. [tex]answer[/tex]

   Step-by-step explanation:

   Let the first term of AP be a and common difference be d.

   a9 = 7a2

   ⇒ a + 8d = 7(a + d) …(i)

   a12 = 5a3 + 2

   ⇒ a + 11d = 5(a + 2d) + 2 …(ii)

   From (i),

   a + 8d = 7a + 7d

   – 6a + d = 0 …(iii)

   From (ii),

   a + 11d = 5a + 10d + 2

   – 4a + d = 2 …(iv)

   Subtracting (iv) from (iii),

   – 2a = – 2

   ⇒ a = 1

   From (iii),

   – 6 + d = 0

   d = 6

   Reply