Question

0
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The first term of an AP. is 100 and the sum of whose first 6 terms is 5 times the sum of the next 6 terms
then the c.d.is -
(a) -10
(b) 10
(0) 5
(d) None of these​

Answer 1

${\huge {\mathfrak {Answer :-}}}$

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Given that,

First term is 100.

And, sum of first six terms is 5 times the sum of next six terms.

Sum of first 6 terms is

= 6a + 15d

= 600 + 15d .

Sum of next six terms is

= 6a + 6d + 7d + 8d + 9d + 10d + 11d

= 6a + 51d

= 600 + 51d

By condition,

$\implies$ (600 + 15d) = 5(600 + 51d)

$\implies$ 120 + 3d = 600 + 51d

$\implies$ 120 - 600 = 51d - 3d

$\implies$ - 480 = 48d

$\implies$ d = - 10

.°. Common difference = (- 10).

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Answer 2

$\underline \mathbb{SOLUTION}$

$\underline \mathbb{GIVEN}$

»1st term is 100.

»The sum of whose first 6 terms is 5 times the sum of the next 6 terms.

Sum of first 6 terms:

$= > 6a + 15d$

$= > 600 + 15d$

Sum of next 6 terms is:

$= > 6a + 6d + 7d + 8d + 9d + 10d + 11d$

$= > 6a + 51d$

$= > 600 + 15d$

$\underline \mathbb{ATQ}$

$= >( 600 + 15d) = 5(600 + 51d)$

$= > 120 + 3d = 600 + 51d$

$= > 120 - 600 = 51d - 3d$

$= > - 480 = 48d$

$d = \frac{ - 480}{48}$

$d = - 10$

COMMON DIFFERENCE = —10

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