The fourth term of an ap is 1 less than twice the second term. If the sixth term is 7, find the first term.

3 answers

Just translate into Math using your definitions of an AP
a+5d = 7 **

a+ 3d = 2(a+d) - 1
a + 3d = 2a + 2d - 1
-a + d = -1 ***

add ** and ***
6d = 6
d = 1
back in **
a + 5=7
a = 2

the first term is 2

check:
sequence is 2,3,4,5,6,7,8, ...
Is the fourth term less than twice the second by 1 ? YES
Is the 6th term equal to 7 ? YES
All is good.
The forth term of an A.P is one less than twice the 2nd term. If the sixth term is 7, find the first term
The first term is 2