Question

if the sum and product of the first three term in A.p are 33 and 1155 respectively,then the value of its 11th term is
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Answer 1

Answer:

11th term can be either 47 or -25

Step-by-step explanation:

Given :

The sum and product of the first three terms in A.P are 33 and 1155 respectively.

To find :

the value of its 11th term

Formula :

nth term of an A.P is given by

$\longmapsto \bf a_n=a+(n-1)d$

where

a denotes first term

d denotes common difference

Solution :

Let the first three terms be (a - d) , a and (a + d)

Their sum = 33

a - d + a + a + d = 33

  3a = 33

  a = 33/3

  a = 11

Their product = 1155

(a - d) (a) (a + d) = 1155

 a (a² - d²) = 1155     [ ∵ (x + y)(x - y) = x² - y² ]

 

Put a = 11,

11(11² - d²) = 1155

 11(121 - d²) = 1155

  121 - d² = 1155/11

  121 - d² = 105

  d² = 121 - 105

  d² = 16

  d = √16

  d = ±4

If d = +4,

first term = 11 - 4 = 7

11th term = 7 + (11 - 1)(4)

    = 7 + 10(4)

    = 7 + 40

    = 47

If d = -4,

first term = 11 - (-4) = 15

11th term = 15 + (11 - 1)(-4)

      = 15 + 10(-4)

      = 15 - 40

      = -25

Therefore, 11th term can be either 47 or -25