Question

In: Math

Write a recursive formula for the arithmetic sequence −2, −7/2 , − 5, −13/2 , … and then find the 22nd term.

Write a recursive formula for the arithmetic sequence −2, −7/2 , − 5, −13/2 , … and then find the 22^nd term.

Expert Solution

Consider an arithmetic sequence,

-2, 7/2, -5, -13/2, …

Use the recursive formula of an arithmetic sequence,

a1

an = an-1 + d, n ≥ 2...... (1)

First term of the given sequence is a1 = -2

Common difference will be computed as follows:

d = a2\r\n– a1

= (-7/2) – (-2)

= -3/2

Substitute d = -3/2 in and simplify,

an = an-1 – 3/2

Therefore, recursive formula for given arithmetic series is,

a1 = -2

an = an-1 -3/2, n ≥ 2

Compute 22nd term of the given sequence using explicit formula of an arithmetic sequence,

an = a1 + (n – 1)d ...... (2)

Substitute a1 = -2, n = 22 and d = -3/2 in (2) and simplify,

a22 = -2 + (22 – 1)(-3/2)

= -2 + 21 × (-3/2)

= -2 – 63/2

= -67/2

Junaid answered 1 year ago

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