Answer:
5
Step-by-step explanation:
The general term of an arithmetic progression is ...
an = a1 +d(n -1)
where a1 is the first term and d is the common difference.
Here we are given that ...
a5 = 3×a2
a5 +a6 +a7 +a8 = 240
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In terms of a1 and d, these tell us ...
a1 +d(5 -1) = 3(a1 +d(2 -1))
a1 +4d = 3a1 +3d . . . . . eliminate parentheses
d = 2a1 . . . . . . . . . . . subtract a1+3d
and ...
(a1 +4d) +(a1 +5d) +(a1 +6d) +(a1 +7d) = 240
4a1 +22d = 240
Substituting for d, we have ...
4a1 +22(2a1) = 240
48a1 = 240
a1 = 240/48 = 5
The first term is 5.
