The 4
th
term of an arithmetic progression is 15, and the 15
th
term is −29. Find the 10
th
term.
- A−5
- B−13
- C−17
- D−9
Solution & Step-by-step Explanation
The general formula for the n
th
term of an Arithmetic Progression (AP) is:
a
n
=a+(n−1)d
where a is the first term and d is the common difference.
Given:
4
th
term (a
4
) = 15⟹a+3d=15 --- (Equation 1)
15
th
term (a
15
) = −29⟹a+14d=−29 --- (Equation 2)
Subtract Equation 1 from Equation 2:
(a+14d)−(a+3d)=−29−15
11d=−44
d=−4
Substitute the value of d into Equation 1:
a+3(−4)=15
a−12=15
a=27
Now, find the 10
th
term (a
10
):
a
10
=a+9d
a
10
=27+9(−4)
a
10
=27−36=−9
th
term of an Arithmetic Progression (AP) is:
a
n
=a+(n−1)d
where a is the first term and d is the common difference.
Given:
4
th
term (a
4
) = 15⟹a+3d=15 --- (Equation 1)
15
th
term (a
15
) = −29⟹a+14d=−29 --- (Equation 2)
Subtract Equation 1 from Equation 2:
(a+14d)−(a+3d)=−29−15
11d=−44
d=−4
Substitute the value of d into Equation 1:
a+3(−4)=15
a−12=15
a=27
Now, find the 10
th
term (a
10
):
a
10
=a+9d
a
10
=27+9(−4)
a
10
=27−36=−9