Question

Find the sum of the first 45 terms of the arithmetic sequence: 7,15,23,31,dots

Answer 1

S₄₅ = 8235

Explanation:

the sum to n terms of an arithmetic sequence is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 7 and d = a₂ - a₁ = 15 - 7 = 8 , then

S₄₅ =
`(45)/(2)` [ ( 2 × 7) + (44 × 8) ]

= 22.5(14 + 352)

= 22.5 × 366

= 8235