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Standard X

Mathematics

General Term of an AP

Given an arit...

Question

Given an arithmetic progression with its first three terms as $2 t, 5 t - 1$ and $6 t + 2$ , for some real number $t$ . Find the value of the fourth term of the sequence.

4

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8

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10

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16

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19

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Solution

The correct option is E $19$

2t, 5t – 1, and 6t + 2 are the first three terms of an arithmetic sequence.

To find the common difference of A.P. third term – second term = second term – first term will give you the value of t.

6t + 2 – 5t + 1 = 5t – 1 - 2t

t + 3 = 3t – 1

2t = 4

t = 2.

Substituting 2 for t in the expressions of the three first terms of the sequence, one

sees that they are 4, 9 and 14, respectively. The common difference between consecutive terms for this arithmetic sequence is 5.

Therefore, the fourth term is 14 + 5 = 19

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Given an arithmetic progression with its first three terms as 2t,5t−1 and 6t+2, for some real number t. Find the value of the fourth term of the sequence.

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