Let un denote the n-th term of an arithmetic sequence. Given u1×u2=10 and u1×u3=16. If the terms of the arithmetic sequence are positive numbers, then u10=....
Explanation
The general form of the n-th term of an arithmetic sequence is un=a+(n−1)b. Then
u1×u2=a×(a+(2−1)b)=10
a(a+b)=10...(1)
And also
u1×u3=a×(a+(3−1)b)
a(a+2b)=16...(2)
Divide equation (1) by (2)
a(a+2b)a(a+b)=1610
a+2ba+b=85
8(a+b)=5(a+2b)
8a+8b=5a+10b
3a=2b
b=23a
Substitute 2b=3a into equation (2)
a(a+2b)=16
a(a+3a)=16
a(4a)=16
4a2=16
a2=4
a=±2
Because the terms are positive then a>0 or what satisfies is a=2. So b=23(2)=3. Then the 10th term of the sequence is
