Question

. The last term of an A.P. is 10 times the first, and the last but one is equal
to sum of the 4th and 5th. Find the number of terms and show that the common
difference is equal to the first term.
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Answer 1

Step-by-step explanation:

last term = 10 × first term

last term - 1 = 4th term + 5 th term

By this you can find the required values.

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Answer 2

a4 = a+3d

a5= a+4d

a4+ a5 = 24

i.e. = a+3d+a+4d=24

=2a+7d=24 (1)

a6= a+5d

a10=a+9d

a6 +a10 =34

i.e. = a+5d+a+9d=34

=2a+14d=34 (2)

Subtracting 2 from 1, we get

7d=10

d=10/7

Substitute d in 1, we get

2a + 7(10/7) = 24

2a+10=24

a=7

therefore, a=7 d =10/7

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