The sum of the first four terms of a linear sequence (A.P.) is 26 and that of the next four terms is 74. Find the value of
(1)the first term
(2) the common difference
a,a+d,a+2d+a+3d
Sums up to 26
4a+6d=26
Boils down to
2a+3d=13
And likewise
a+4d,a+5d,a+6d,a+7d
Sums up to 74
4a+22d=74
Boils down to
2a+11d=37
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2a+3d=13......(*)
2a+11d=37......(**)
Subtract (*) from (**)
8d=24
d=3
Now find a
And you're done