From simple questions to complex issues, IDNLearn.com has the answers you need. Our Q&A platform offers reliable and thorough answers to ensure you have the information you need to succeed in any situation.
Sagot :
Answer:
S₁₃ = 455
Step-by-step explanation:
the sum to n terms of an arithmetic 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
We require to find both a₁ and d
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₄ = 20 and a₁₃ = 65 , then
a₁ + 3d = 20 → (1)
a₁ + 12d = 65 → (2)
subtract (1) from (2) term by term to eliminate a₁
9d = 45 ( divide both sides by 9 )
d = 5
substitute d = 5 into (1) and solve for a₁
a₁ + 3(5) = 20
a₁ + 15 = 20 ( subtract 15 from both sides )
a₁ = 5
Then
S₁₃ = [tex]\frac{13}{2}[/tex] [ (2 × 5 ) + (12 × 5 ) }
= 6.5 (10 + 60)
= 6.5 × 70
= 455
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.