1
Question
If an AP, the sum of first ten term is -150 and the sum of its next ten terms is -550. Find first term of AP.
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Solution
Sum of n terms(Sn)=n2[2a+(n−1)d]
a= First termd= Common differencen= number of terms
GivenS10=−150S20−S10=−550S20=−550−150S20=−700S10=102[2a+(10−1)d]=−1502a+9d=−30eq__(1)
S20=−700202[2a+19d]=−7002a+19d=−70eq____(2)
From equations-(1) & (2)
2a+9d=−30
2a+19d=−70
−10d=40
d=−4
2a+9d=−30
2a=−30−36
a=−33
Sum of n terms(Sn)=n2[2a+(n−1)d]
a= First term
d= Common difference
n= number of terms
Given
S10=−150S20−S10=−550S20=−550−150S20=−700S10=102[2a+(10−1)d]=−1502a+9d=−30eq__(1)S20=−700202[2a+19d]=−7002a+19d=−70eq____(2)
From equations-(1) & (2)
2a+9d=−30
2a+19d=−70
−10d=40
d=−4
2a+9d=−30
2a=−30−36
a=−33
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