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# Given the sequence above, what is the sum of the 10th and the 20th

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 02:09
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Difficulty:

5% (low)

Question Stats:

87% (01:38) correct 13% (01:45) wrong based on 118 sessions

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8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

Kudos for a correct solution.

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Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 04:16
1
Bunuel wrote:
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

Kudos for a correct solution.

GIven sequence = 8,19,30,41,52....

Thus $$S_n = S_{n-1} + 11$$

$$S_{10} = S_1+(10-1)*11 = 8+9*11$$
$$S_{20} = S_1+(20-1)*11= 8+19*11$$

Thus the sum = 8+9*11+ 8+19*11 = 16+11(20+8) = 16+220+88 = 220+104 = 324. A is the correct answer.
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Re: Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 04:41
1
8, 19, 30, 41, 52, ...

a = 8, d = 11.

10th term = a+9d = 8+9*11 = 107
20th term = a+21d = 8+19*11 = 217

sum = 107+217 = 324. Ans (A).
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Re: Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 05:38
1
Bunuel wrote:
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

Kudos for a correct solution.

This is an Arithmatic progression with First term 8 and Common Difference = 19-8 = 30-19 = 11

10th Term = First term + 9*Common Difference = 8+9*11 = 107

20th Term = First term + 19*Common Difference = 8+19*11 = 217

Difference = 217 + 107 = 324

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Re: Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 05:48
1
Bunuel wrote:
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

Kudos for a correct solution.

The terms are in A.P
a=8, d=11
a10=a+9d=8+9(11)=107
And, a20=a+19d=9+19(11)=217
Therefore, a10+a20=107+217=324
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Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 12:59
1
Bunuel wrote:
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

Kudos for a correct solution.

First term a =8
Difference btw two consecutive terms = 11

Formula to calculate nth term when the seq is A.P is = a + (n-1)* d

10th term = 8 + (10-1) * 11 = 107
20th term = 8 + (20-1) * 11 = 217

Sum = 107+217 = 324

Option A
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Re: Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 17:06
1
The series has numbers spaced out by 11. So the equation can be written as 8+ 11(n-1).

The 10th number will be - 8+11(9) = 107
20th number - 8+11(19) = 217

Sum is 324, hence answer is A

Bunuel wrote:
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

Kudos for a correct solution.

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aimtoteach

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Joined: 11 Dec 2013
Posts: 7
Re: Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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22 Jul 2015, 23:43
1
This is a case of AP with following :
first term=8, difference=11.

To find the 10th term, use the following formula:
nth term==a+(n-1)*d, where a==first term, n==number of terms, d==difference

10th term = 8 + (10-1) * 11 ==107
20th term = 8 + (20-1) * 11 ==217

Sum of 10th and 20th term = 107 + 217 == 324. A is correct answer

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Naresh Mittal
Math Expert
Joined: 02 Sep 2009
Posts: 58445
Re: Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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26 Jul 2015, 12:08
Bunuel wrote:
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

Kudos for a correct solution.

800score Official Solution:

First, we need to derive a formula so that we do not need to write out the first 20 terms.
The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 10th term is 10 × 11 – 3 = 107.
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 324.

The correct answer is choice (A).
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Re: Given the sequence above, what is the sum of the 10th and the 20th  [#permalink]

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16 Dec 2018, 18:58
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Re: Given the sequence above, what is the sum of the 10th and the 20th   [#permalink] 16 Dec 2018, 18:58
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