Question

The first 5 terms of a sequence are 2 8 14 20 26 Find the nth term ​

Answer 1

Given sequence :-

• 2 , 8 , 14 , 20 , 26...

Solution :-

We need to calculate the nth term of the given sequence.

• Common difference (d) = 8 - 2 => 6
• First term of sequence (a) = 2

We know that,

• tn = a + (n - 1) d

Applying the values here.

>> tn = 2 + (n - 1) 6

>> tn = 2 + (n - 1) × 6

>> tn = 2 + 6n - 6

>> tn = 6n - 4

Therefore, nth term of the sequence is (6n - 4).

Answer 2

Answer:
`\Large\boxed{a_n=6n-4}`

Explanation:

Given sequence

2, 8, 14, 20, 26

Determine the pattern

2 + 6 = 8

8 + 6 = 14

14 + 6 =20

20 + 6 = 26

For each term, add 6 to get the next term

Determine the type of sequence

Since it continuously adds 6, the common difference is 6, which means it is an arithmetic sequence

Given the arithmetic sequence formula

aₙ = a₁ + d (n - 1)

• a₁ = 1st term of a sequence

• aₙ = nth term of a sequence
• n = nth position
• d = Common difference

Substitute values into the formula

aₙ = (2) + (6) (n - 1)

aₙ = 2 + 6 (n - 1)

aₙ = 2 + 6n - 6

aₙ = 2 - 6 + 6n

`\Large\boxed{a_n=6n-4}`

Hope this helps!! :)

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