Question

Consider the arithmetic sequence 17, 20, 23, 26,….. a. Write the algebraic form of this sequence. b. Is 400 a term of this sequence?​

Answer 1

17, 20, 23, 26 is an arithmetic progression.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence:

an = a1 + ( n - 1 ) * d

In this case the initial term a1 = 17, the common difference d = 3

an = a1 + ( n - 1 ) * d

an = 17 + ( n - 1 ) * 3

an = 17 + 3 * n - 3 * 1 = 17 + 3 n - 3 = 14 + 3 n = 3 n + 14

Answer 2

The answers (a) a$_{n}$ = 14 + 3n

                       (b) 400 is not a term of AP

Given: 17, 20, 23, 26 .. is a Arithmetic series  

To find: Algebraic form of sequence and check if 400 is a term of sequence

Solution: 17, 20, 23, 26 .. is a Arithmetic series

⇒ First term a = 17 and common difference d = 20 - 17 = 3

Algebraic form of Arithmetic sequence

⇒  a$_{n}$ = a + d(n-1)

⇒  a$_{n}$ = 17 + 3(n-1)

⇒  a$_{n}$ = 17 + 3n - 3

⇒  a$_{n}$ = 14 + 3n  

Algebraic form of Arithmetic sequence is  a$_{n}$ = 14 + 3n

Assume that nth term of the sequence is 400

⇒  a$_{n}$ must be equal to 400

⇒  14 + 3n = 400

⇒  3n = 386

⇒  n = 128.666  is not possible      

400 will not present in the sequence

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