An arithmetic sequence is given as 5, 11, 17, ………, 599.

(i) state the values of ‘a’, the first term of the sequence

[2 marks]

(ii) find the value of ‘d’, the common difference of the sequence

[2 marks]

find t15, the 15th term of the sequence
[3 marks]

find the total number of terms, n, in the sequence, where 599 is the last term
[4 marks]

find the sum of all the terms of the sequence

Answer and explanation:

Given : An arithmetic sequence is given as 5, 11, 17, ………, 599.

An arithmetic series is in the form

Where, a is the first term and d is the common term.

(i) State the values of ‘a’, the first term of the sequence

The first term in the given sequence is a=5

(ii) Find the value of ‘d’, the common difference of the sequence

The common difference of the given sequence is d=11-5=6

(iii) Find T15, the 15th term of the sequence

The nth term of the sequence is given by,

(iv) Find the total number of terms, n, in the sequence, where 599 is the last term

Last term l=599 , a=5 , d=6

Applying last term formula,  

(v) Find the sum of all the terms of the sequence

a=5 , d=11, l=599 , n=100

The sum of the sequence is given by,

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step-by-step explanation:

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