Question

the 12th term of a g.p. whose first term is 1/8 & second term is 1/2 is .......

Answer 1

Given,

Without actual division, find out the quotient when the sum of numbers 167, 716 and 671 is divided by:

(a)37

(b) 111

By adding 167 + 716 + 671 = 1554

Now we know that by expanding the numbers we can write as

➠ 167 = 1 x 100 + 6 x 10 + 7

➠ 716 = 7 x 100 + 1 x 10 + 6

 ➠ 671 = 6 x 100 + 7 x 10 + 1

Now,

⟾ 167 + 716 + 671  

⟾ 1 x 100 + 6 x 10 + 7 + 7 x 100 + 1 x 10 + 6 + 6 x 100 + 7 x 10 + 1

⟾  (1 + 7 + 6)100 + (6 + 1 + 7)10 + (7 + 6 + 1) 14 x 100 + 14 x 10 + 14

⟾ 14(100 + 10 + 1)

⟾  14 x 111

⟾  14 x 3 x 37 (3 x 37 = 111)

⟾ 42 x 37

So quotient is 42 when 1554 is divided by 37.

Similarly for 111 we get

⟾  14 x 1 x 111

⟾  14 x 111  

So quotient is 14 when 1554 is divided by 111

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Answer 2

The 12th term is 2×4⁹.

Given,

    $a_1 = \frac{1}{8} , a_2 = \frac{1}{2}$

∴ $r = \frac{a_2}{a_1}$

      $= \frac{\frac{1}{2} }{\frac{1}{8} }$

        = 4

Thus, the 12 th term in the given GP is a₁₂ = ar¹¹

                                                                      = $\frac{1}{8}$ x 4¹¹

                                                                      = $\frac{4 . 4. 4^9}{8}$

                                                                      = 2 x 4⁹

Hence the 12th term of the given geometric progression is 2×4⁹.

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