Question

The first three terms of an arithmetic sequence are 2k-7; k+8 and 2k-1.
Calculate the value of the 15th term of the sequence.​

Answer 1

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The first three terms of an arithmetic sequence are 2k-7; k+8 and 2k-1.

Calculate the value of the 15th term of the sequence.

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Given:-

a = 2k - 7

a₂ = k + 8

a₃ = 2k - 1

Solution :-

As we know that,

a₃ = a + 2d

So, 2k - 1 = 2k -7 + 2d

2d = 6

d = 3

Again, put value of d in equation,

a₂ = a + d

k + 8 = 2k - 7 + 3

2k - k = 8 + 7 -3

k = 15 - 3

k = 12

⇒ a = 2k - 7

a = 2(12) - 7

a = 24 - 7

a = 17

Now 15th term of sequence will be,

aₙ = a + (n-1)d

a₁₅ = a + (n-1)d

a₁₅ = 17 + (15-1)3

a₁₅ = 17 + (14)3

a₁₅ = 17 + 42

a₁₅ = 59

Therefore, the value of 15th term of the sequence is 59.

Answer 2

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