Question

the 7th term of an ap is 5 times the first term and its and term exceeds twice the first term by 1 the first term of the ap is
(a) 151 (b) -39 (c) 3 (d) -124​

Answer 1

Explanation :-

Given that,

For an A.P,

First term = T₁

Common difference = d

Also, T₇ = 5 × T₁

or, T₁ + (7 - 1)d = 5T₁

or, 4T₁ = 6d

or, T₁ = 3d (1)

2

Again, T₃ = 2 × T₁ + 1

or, T₁ + (3 - 1)d = 2T₁ + 1

or, T₁ + 2d = 2T₁ + 1

or, 2d = (3d/2) + 1 [From the relation (1)]

or, d = 2

So, T₁ = (3d/2) = 3

Hence, the first term of the given A.P is 3.

Hope you liked my solution

Pls mark me as brainliest

Thanks.