Question

The ninth term of an A.P. is equal to the seventh times the second term and the twelfth term exceeds five times the third term by 2. Find the first term and the common difference?

Answer 1

Answer:

6

Step-by-step explanation:

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Answer 2

Answer:

Let the first term of A.P. be 'a' and the common difference be 'd'

Given,

a₉ = 7a₂

or, a+8d = 7(a+d)  ________(i)

and

a₁₂  = 5a₃ + 2

or, a+11d = 5(a+2d) + 2   ________(ii)

from eq. (i)

a+8d = 7a+7d

-6a + d = 0   ________(iii)

from eq. (ii)

a+11d = 5a+10d + 2

-4a + d = 0   ________(iv)

Substracting eq. (iv) from eq. (iii), we get,

-2a = 2

a = 1

or,

from eq. (iii)

-6a + d = 0

d = 6

Hence,

First term is 1

Common difference is 6