The first and last terms of an arithmetic progression are 32 and −43. If the sum of the series is −88, then it has how many terms?
- A16
- B15
- C17
- D14
Solution & Step-by-step Explanation
The formula for the sum of an arithmetic progression (S
n
) when the first term (a) and the last term (l) are known is:
S
n
=
2
n
(a+l)
Given:
a=32
l=−43
S
n
=−88
Substitute these values into the formula:
−88=
2
n
(32+(−43))
−88=
2
n
(−11)
Multiply both sides by 2:
−176=−11n
Divide by −11:
n=
−11
−176
=16
Thus, the progression has 16 terms.
n
) when the first term (a) and the last term (l) are known is:
S
n
=
2
n
(a+l)
Given:
a=32
l=−43
S
n
=−88
Substitute these values into the formula:
−88=
2
n
(32+(−43))
−88=
2
n
(−11)
Multiply both sides by 2:
−176=−11n
Divide by −11:
n=
−11
−176
=16
Thus, the progression has 16 terms.