Question

In: Math

Write a recursive formula for the arithmetic sequence 0, −1/2 , −1, −3/2 , … , and then find the 31st term.

Write a recursive formula for the arithmetic sequence 0, −1/2 , −1, −3/2 , … , and then find the 31^st term.

Expert Solution

Consider the arithmetic sequence,

0, -1/2, -1, -3/2 …

Use the recursive formula for an arithmetic sequence,

a1

an = an-1 + d ...... (1)

First term of the sequence is a1 = 0

Compute common difference as follows:

d = a2 – a1

= 1/2 – 0

= -1/2

Substitute d = -1/2 in the formula (1) an = an-1 + d and simplify,

an = an-1 – 1/2

Therefore, recursive formula for given arithmetic sequence is,

a1 = 0

an = an-1 -1/2, n ≥ 2

Consider the explicit formula for the nth term of an arithmetic sequence as

an = a1 + (n – 1)d …... (2)

Compute 31st term of the given sequence, substitute a1 = 0, n = 31 and d = -1/2 in equation (2) an = a1 + (n – 1)d and simplify,

a31 = a1 + (31 – 1)d

= 0 + 30 × (-1/2)

= 0 - 15

Therefore, 31st term of the given sequence is a31 = -15.

Junaid answered 1 year ago

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