Question

Find a formula for the general term of the following sequence,
60,67,74,81,88
Please help me out in this question.​

Answer 1

Step-by-step explanation:

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Answer 2

Hence, the general term of the given sequence is 53 + 7n.

Given:

The sequence 60, 67, 74, 81, 88.

To Find:

The general term for the given sequence.

Solution:

A sequence is said to be in arithmetic progression if the difference between every two consecutive terms is the same.

We have been given a sequence 60, 67, 74, 81, 88.

Let us find out the difference between each of the consecutive terms.

67 - 60 = 7, 74 - 67 = 7, 81 - 74 = 7, 88 - 81 = 7.

We observe that the difference between each of the consecutive terms is the same, and hence, the given sequence is in AP where:

The first term , a = 60.

The common difference, d = 7.

The general representation of the series is given by its $n^{th}$ term .

The $n^{th}$ term of an AP, $a_{n}$ = a + (n - 1)d

$a_{n}$ =60 + (n - 1)x7 = 60 + 7n -7 = 53 + 7n.

⇒ $a_{n}$ = 53 + 7n.

Hence, the general term of the given sequence is 53 + 7n.

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