Answer:
S₁₅ = 645
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Using the nth term formula [tex]a_{n}[/tex] = 5n + 3 , then
a₁ = 5(1) + 3 = 5 + 3 = 8
a₂ = 5(2) + 3 = 10 + 3 = 13 , then
d = a₂ - a₁ = 13 - 8 = 5
Thus
S₁₅ = [tex]\frac{15}{2}[/tex] [ (2 × 8) + (14 × 5) ]
= 7.5( 16 + 70)
= 7.5 × 86
= 645
