Question

with step by step explanation ​

Answer 1

Step-by-step explanation:

The required A.P is

2, 5, 8, 11........................

Step-by-step explanation:

Formula used:

The n th term of the A.P a, a+d, a+2d, .......

is

t_n=a+(n-1)dt

n

=a+(n−1)d

\begin{lgathered}Given:t_7=4\:t_2\\\\a+6d=4[a+d]\\\\3a-2d=0.........(1)\end{lgathered}

Given:t

7

=4t

2

a+6d=4[a+d]

3a−2d=0.........(1)

\begin{lgathered}Also,\\\\t_12=3\:t_4+2\\\\a+11d=3(a+3d)+2\\\\a+11d=3a+9d+2\\\\2a-2d=-2.........(2)\end{lgathered}

Also,

t

1

2=3t

4

+2

a+11d=3(a+3d)+2

a+11d=3a+9d+2

2a−2d=−2.........(2)

Now we solve (1) and (2)

3a-2d=0.........(1)

2a-2d=-2.........(2)

(1)-(2)

a=2

using a=2 in (1) we get

3(2)-2d=0

2d=6

d=3

The required A.P is

2, 5, 8, 11........................

Answer 2

Answer:

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