Question

Find the A.P. whose 1st term is 100 and the sum of the first six terns is 5 times
the sum of the next six terms.​

Answer 1

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Answer 2

GIVEN :–

• First term of A.P. is 100.

• The sum of the first six terms is 5 time of the sum of the next six terms.

SOLUTION :–

• Let the first term & common difference are a & d respectively.

• So , First 12 terms of A.P. are a , a+d , a+2d , a+3d , a+4d , . . . . , a+11d.

• According to the question –

=> [a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d)] = 5[(a+6d) + (a+7d) + (a+8d) + (a+9d) + (a+10d) + (a+11d)]

⇛ 6a + 15d = 5(6a + 51d)

⇛ 6a + 15d = 30a + 255d

⇛ -24a = 240d

⇛ d = - (24/240)a

⇛ d = - (1/10)a

⇛ d = - (1/10)(100)

⇛ d = - 10

• Hence , The A.P. 100 , 90 , 80 , 70, . . . . . .