# In an Arithmetic progression the 4th term is 3 times the first term and the 7th term is one more than the twice the third term find the sequenve

2
by appi

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by appi

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t7=1+t3

so

a+3d=3a.......................1

a+6d=1+a+2d.....................2

2a=3d

4d=1

so d=1/4

2a=3/4

a=3/8

s0

3/8,5/8,7/8,9/8,....................

according to the question

t₄=3*t₁

a+3d=3a

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

t₇=2t₃+1

a+6d=2(a+2d)+1

a+6d=2a+4d+1

a-2d=1..............2

on solving 1 and 2

we get

a=3 and d=2

therefore the sequence is 3,5,7,9.................