Question

the general term of the sequence is given by an = -4n + 15 . Is this the sequence of an AP? if so find the 15th term and common difference?

Answer 1

HELLO DEAR,

GIVEN:-

the general term of the sequence is given by $\bold{a_n = -4n + 15}$

now,

put n = 1,

$\bold{a_1 = -4(1) + 15 = -4 + 15 = 11}$

n = 2,

$\bold{a_2 = -4(2) + 15 = -8 + 15 = 7}$

n = 3 ,

$\bold{a_3 = -4(3) + 15 = -12 + 15 = 3}$

we can consider these terms are in ap,

whose first term = 11 , common difference = (7 - 11) = -4

now, the 15th terms is

put n = 15 the equation,

$\bold{a_{15} = -4(15) + 15 = 15 \times (-3) = -45}$

also, we can find by n the terms foumula,

we know:-

$\boxed{\bold{a_n = a + (n - 1)d}}$

$\bold{a_{15} = 11 + (15 - 1)(-4)}$

$\bold{a_{15} = 11 - 56}$

$\bold{a_{15} = -45}$

I HOPE ITS HELP YOU DEAR,

THANKS