In an arithmetic progression, the 10th term is 11 and the 11th term is

Question

In an arithmetic progression, the 10th term is 11 and the 11th term is 10.How many consecutive terms(starting from the first term) of the arithmetic progression should be considered so as to make their sum equal to zero?
A.33
B.41
C.37
D.39
E.42

nick1816 · Answer

10 th term of the sequence = a+9d = 11

11th term of the sequence = a+10d= 10

We get, d = -1; a= 20

21st term of the sequence = a+20d = 20+(20*-1) = 0

Since we want our sum equals to 0, Mean of the terms or middle term must be 0. Hence middle term of the sequence must be 21st.

Total number of terms = 21*2 -1 =41

GunjanMadan1 · Answer

nth term in an arithmetic progression= a+(n-1)d

11=a+9d
10=a+10d

solving above provides a=20 and d=-1

Sum of A.P Series = n/2*{2a+(n-1)d}

0= n/2*{40-n+1}

n=41 (B)

GMATinsight · Answer

10th Term = 11
11th Term = 10

i.e. Common Difference = -1

1st term will be 9 more than 11 i.e. 20

Sum of consecutive numbers will be zero when the series goes from +20 to -20 i.e. 41 terms

Answer: Option B

Kinshook · Answer

Given: In an arithmetic progression, the 10th term is 11 and the 11th term is 10.
Asked: How many consecutive terms(starting from the first term) of the arithmetic progression should be considered so as to make their sum equal to zero?

Let a be the first term and d be common difference of the arithmetic progression

a + 9d = 11
a + 10d = 10
d = -1
a = 20

a + 20d = 0
Sn = n/2(2a + (n-1)d)
2a + 40d = 0
n-1 =40
n = 41

IMO B

MathRevolution · Answer

10th term = a + 9d = 11
11th term = a + 10d = 10

Therefore, d = -1 and a = 20. (after subtracting 1 equation from another).

=> With a = 20 and d = -1 for sum to be zero, we need progression like: 20 , 19 , ...... 0, -1 , -2 ,....... -19, -20.

Hence, there will be 41 terms.

Answer B

Paras96 · Answer

In an arithmetic progression, the 10th term is 11 and the 11th term is 10.How many consecutive terms(starting from the first term) of the arithmetic progression should be considered so as to make their sum equal to zero?
A.33
B.41
C.37
D.39
E.42

a10=a + 9d=11
a11=a+10d=10
=> d = -1
=> a = 20

For sum =0, the sum of first and last term must be equal to zero, hence
Therefore,
=> a + an =0
=> 20 + 20 + (n-1)*-1 = 0
=> 40 = n-1
=> n = 41

Hence B

In an arithmetic progression, the 10th term is 11 and the 11th term is

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In an arithmetic progression, the 10th term is 11 and the 11th term is

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