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# In a certain sequence, the term an is defined by the formula

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

In a certain sequence, the term an is defined by the formula [#permalink]  27 Jul 2018, 07:15
Expert's post
00:00

Question Stats:

75% (00:42) correct 25% (00:00) wrong based on 4 sessions
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
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

Re: In a certain sequence, the term an is defined by the formula [#permalink]  12 Aug 2018, 05:33
Expert's post
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 $$= 186 \times 75 = 13,950$$.
_________________

Sandy
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Re: In a certain sequence, the term an is defined by the formula   [#permalink] 12 Aug 2018, 05:33
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