Question

If the 8th term of A.P. is 31th and 15th term of the A.P. is 59, the its comon difference is
(a) 3
(b) 4
(c) 1/4
(d) 3/4

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Answer 1

Question:-

If the 8th term of A.P. is 31th and 15th term of the A.P. is 59, the its comon difference is

Solution:-

Given,

• 8th term is 31
• 15th term is 59

➣ tn = a + ( n - 1 ) d

➣ 31 = a + ( 8 - 1 ) d

➣ 31 = a + 7d .......... ( 1 )

➣ tn = a + ( n - 1 ) d

➣ 59 = a + ( 15 - 1 ) d

➣ 59 = a + 14d .......... ( 2 )

Now,

( 2 ) - ( 1 )

59 = a + 14d .......... ( 2 )

-31 =-a ±7d .......... ( 1 )

__________________________

28 = 7d

➣ d = 28/7

➣ $\boxed{d \: = 4}$

Now,

Substitute d in the equation ( 1 ) to get first term:-

➣ 31 = a + 7d

➣ 31 = a + 7(4)

➣ 31 = a + 28

➣ a = 31 - 28

➣ $\boxed{a\: =\: 3}$

Verification:-

➣ 31 = a + 7d

➣ 31 = 3 + 7(4)

➣ 31 = 3 + 28

➣ 31 = 31