Answer:
see explanation
Step-by-step explanation:
the n th term of an arithmetic sequence is
=
+ (n - 1)d
given = 3 and
= 10, then
= 3 + d = 10 ⇒ d = 10 - 3 = 7
= 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4
the sum to n terms of an arithmetic sequence is
=
[2
+ (n - 1)d ]
= [(2 × 3) + 7(n - 1) ]
= (6 + 7n - 7 )
= (7n - 1)
= n² -
n
Answer:
Step-by-step explanation:
Increasing the side length by 5 is represented as s + 5. To get the area of a square we multiply side times side:
The area of a square is s². If we are increasing this area s² by 895, then to represent this we have s² + 895.
Put that together into an equation:
and simplify to
10s = 870 so
s = 87
Let's check that. The area before the addition to the side is 87*87 = 7569; the area after the addition of 5 cm is 92*92 = 8464. The difference is
8464 - 7569 = 895 so we did good!