The general term of a sequence is given by $a_n = -4n + 15$. Is the sequence an A.P.? If so, find its 15th term and the common difference.

Given:

The general term of a sequence is given by $a_n = -4n + 15$.

To do:

We have to check whether the sequence defined by $a_n = -4n + 15$ is an A.P. and find its 15th term and common difference.

Solution:

To  check whether the sequence defined by $a_n = -4n + 15$ is an A.P., we have to check whether the difference between any two consecutive terms is equal.

Let us find the first few terms of the sequence by substituting $n=1, 2, 3....$

When $n=1$,

$a_1=-4(1)+15$

$=-4+15$

$=11$

$a_2=-4(2)+15$

$=-8+15$

$=7$

$a_3=-4(3)+15$

$=-12+15$

$=3$

$a_4=-4(4)+15$

$=-16+15$

$=-1$

Here,

$d=a_2-a_1=7-11=-4$

$d=a_3-a_2=3-7=-4$

$d=a_4-a_3=-1-3=-4$

$d=a_2-a_1=a_3-a_2=a_4-a_3$

The 15th term of the sequence is given by $a_{15}$.

$a_{15}=-4(15)+15$

$=-60+15$

$=-45$

Hence, the given sequence is an A.P. The 15th term is $-45$ and the common difference is $-4$. 

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Updated on: 10-Oct-2022

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