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the sequence has 100 term and the listing of number were as follow x, 7, 11, 15.......... 399 find the value of x​

User Hakan Baba
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1 Answer

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24 votes

Answer:

x = 3

Explanation:

Given the sequence x, 7, 11, 15, ... 399, where 399 is the 100th term, you want to know the first term, x.

Arithmetic sequence

The differences of the first few terms are ...

11 -7 = 4

15 -11 = 4

This suggests an arithmetic sequence with a common difference of 4.

The first term, x, will be 4 less than the second term:

x +4 = 7

x = 7 -4 = 3

The value of x is 3.

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Check

The n-th term of an arithmetic sequence with first term a1 = 3 and common difference d = 4 is ...

an = a1 +d(n -1)

an = 3 +4(n -1) = 4n -1

Then the 100th term is ...

a100 = 4(100) -1 = 399 . . . . consistent with the given information

User Ryeager
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