Question

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.

Answer 1

Given the sequence which is defined by.

$a_n=-4n+15.....eq\left(1\right)$

and we know that nth term of an A.p is given by

$a_n=a+(n-1)d$

which can also be written as

$a_n=a-d+nd.....eq\left(2\right)$

comparing eq(1) and eq(2) we get

common difference is

$d=-4\left(bycomparingcoefficientsofn\right)$

and

$a-d=15$

by putting value of d=5 in above equation we get

$a-(-4)=15$

$⟹a=15-4$

$⟹a=11$ (first term of A.P)

since this sequence has common difference (d=-4) hence it forms an A.P

for finding the 15th term put n=15 in eq(1)

$a_{15}=-4\times 15+15$

$a_{15}=-60+15$

$a_{15}=-45$