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The first and last term of a linear sequence (AP) are 6 and 10 respectively. If ...


Question

The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms.

Options

A) nth = 3

B) nth = 4

C) nth = 5

D) nth = 6

The correct answer is C.

Explanation:

Nth term of a linear sequence (AP) = a+(n − 1)d
first term = 6, last term = 10 sum − 40
i.e. a = 6, l = 10, S = 40
sn = n ÷ 2(2a + (n − 1)d or Sn = ÷2 (a + b)
Sn = n ÷ 2(a + l)
40 = n ÷ 2(6 + 10)
40 = 8n
8n = 40
8n = 40
N = 40/8
= 5
The nth term = 5

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Dicussion (1)

  • Nth term of a linear sequence (AP) = a+(n − 1)d
    first term = 6, last term = 10 sum − 40
    i.e. a = 6, l = 10, S = 40
    sn = n ÷ 2(2a + (n − 1)d or Sn = ÷2 (a + b)
    Sn = n ÷ 2(a + l)
    40 = n ÷ 2(6 + 10)
    40 = 8n
    8n = 40
    8n = 40
    N = 40/8
    = 5
    The nth term = 5

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