GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In a certain sequence, the term an is defined by the formula
[#permalink]
27 Jul 2018, 07:15
27 Jul 2018, 07:15
4
Expert Reply
1
Bookmarks
00:00
Question Stats:
91% (01:55) correct
8% (03:02) wrong based on 103 sessions
Hide Show timer Statistics
In a certain sequence, the term \(a_n\) is defined by the formula \(a_n = a_{n – 1} + 5\) for each integer \(n ≥ 2\). If \(a_1 = 1\), what is the sum of the first 75 terms of this sequence?
(A) 10,150
(B) 11,375
(C) 12,500
(D) 13,950
(E) 15,375
(A) 10,150
(B) 11,375
(C) 12,500
(D) 13,950
(E) 15,375
Re: In a certain sequence, the term an is defined by the formula
[#permalink]
12 Aug 2018, 05:33
12 Aug 2018, 05:33
1
Expert Reply
2
Bookmarks
Explanation
This is an arithmetic sequence: each new number is created by adding 5 to the previous number in the sequence.
Calculate the first few terms of the sequence: 1, 6, 11, 16, 21, and so on.
Arithmetic sequences can be written in this form: \(a_n = a_1 + k(n - 1)\), where k is the added constant and n is the number of the desired term. In this case, the function is: \(a_n = 1 + 5(n - 1)\).
The 75th term of this sequence is \(a_{75} = 1 + 5(74) = 371\).
To find the sum of an arithmetic sequence, multiply the average value of the terms by the number of terms.
The average of any evenly spaced set is equal to the midpoint between the first and last terms.
The average of the 1st and 75th terms is \(\frac{1+371}{2}= 186\). There are 75 terms. Therefore, the sum of the first 75 terms \(= 186 \times 75 = 13,950\).
This is an arithmetic sequence: each new number is created by adding 5 to the previous number in the sequence.
Calculate the first few terms of the sequence: 1, 6, 11, 16, 21, and so on.
Arithmetic sequences can be written in this form: \(a_n = a_1 + k(n - 1)\), where k is the added constant and n is the number of the desired term. In this case, the function is: \(a_n = 1 + 5(n - 1)\).
The 75th term of this sequence is \(a_{75} = 1 + 5(74) = 371\).
To find the sum of an arithmetic sequence, multiply the average value of the terms by the number of terms.
The average of any evenly spaced set is equal to the midpoint between the first and last terms.
The average of the 1st and 75th terms is \(\frac{1+371}{2}= 186\). There are 75 terms. Therefore, the sum of the first 75 terms \(= 186 \times 75 = 13,950\).
Re: In a certain sequence, the term an is defined by the formula
[#permalink]
06 Jul 2019, 00:41
06 Jul 2019, 00:41
sandy wrote:
In a certain sequence, the term an is defined by the formula an = an – 1 + 5 for each integer n ≥ 2. If \(a_1 = 1\), what is the sum of the first 75 terms of this sequence?
(A) 10,150
(B) 11,375
(C) 12,500
(D) 13,950
(E) 15,375
(A) 10,150
(B) 11,375
(C) 12,500
(D) 13,950
(E) 15,375
any other way to solve? Please but not like Manhattan 5lb.
