Question

find the 15th term of the sequence if a8=5 and a21 = -60

Answer 1

Answer:

a8=5

5=a+7d (eq 1)

a21=-60

-60=a+20d (eq 2)

subtracting eq1 from eq2

-65=13d

d=-5

since, a8=a+7d=5

a8=a+7×-5=5

=a-35=5

=a=40

a15=a+14d

=40+14×(-5)

=40-70

=-30

therefore, a15=-30

Answer 2

Given: a^8 = 5 and a^21 = -60 of a sequence

To find: 15th term of the sequence

Solution: The formula for a particular term in the sequence = a + (n - 1)d

Hence according to the question,

a^8 = 5

⇒ a + (8-1)d = 5

⇒ a + 7d =5 [equation i]

a^21 = -60

⇒ a + (21 - 1)d = -60

⇒ a + 20d = -60 [equation ii]

Now subtracting equation i from equation ii,

13d = -65

⇒ d = -5

Putting the value of d in equation i,

a + 7(-5) = 5

⇒ a = 5 +35 = 40

Hence, the 15th term of the sequence = a^15

= 40 + (15 -1)(-5)

= 40 -70

= -30

Answer: -30