The arithmetic sequence ai is defined by the formula: a 1 =15 a i =a i-1 -7 Find the sum of the first 660 terms in the sequence.

The sum of the first 660 terms in the sequence=−1512390

Step-by-step explanation:

We are given that an arithmetic sequence

We have to find the sum of first 660 terms

Substitute i=2

Substitute i=3

Now, the common difference

Now, sum of n terms of an A.P

Substitute n=660, d=-7, a=15

Hence, the sum of the first 660 terms in the sequence=−1512390

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)