if 10times the 10th term of AP is equal to 5 times of 5th term then find 15th term
Answers
Answer:
Step-by-step explanation :
Given,
5 times the 5th term of an AP is equal to 10 times its 10th term
To find,
15th term of the AP
Solution,
we know,
nth term of an AP is given by,
\boxed{\bf a_n=a+(n-1)d}an=a+(n−1)d
where
a - first term
d - common difference
5th term :
a₅ = a + (5 - 1)d
a₅ = a + 4d
10th term :
a₁₀ = a + (10 - 1)d
a₁₀ = a + 9d
According to the question,
5 × a₅ = 10 × a₁₀
5 ( a + 4d ) = 10 ( a + 9d )
5a + 20d = 10a + 90d
10a - 5a = 20d - 90d
5a = -70d
a = -70d/5
a = -14d
a + 14d = 0
we have to find the 15th term
a₁₅ = a + ( 15 - 1 )d
a₁₅ = a + 14d
a₁₅ = 0
∴ 15th term of the AP = 0
Answer:
0
Step-by-step explanation:
We know that,
an=a+(n-1)d , where an is the nth term of the Ap.
a10 =a+(10-1)d
=a+9d-----------------------(1)
a5= a+(5-1)d
=a+4d-----------------------(2)
According to question
10×a10=5×a5
from 1&2
10×(a+9d) = 5×(a+4d)
10a+90d =5a+20d
10a-5a+90d-20d=0
5a+70d =0
5(a+14d)=0
a+14d =0
a+(15-1)d =0
a15=0
15th term is 0.