An AP consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is
A.6 B.5
C.4 D.3
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Answered by
8
Let the first term be - a
then given that there is 23 terms. so to find middle term of an Ap or median of ungrouped data we have
middle term = n+1/2 th term .
so 23+1/2 = 12
now ,
the three middle terms will be a+10 d , a+11 d , a+10 d
given - a+10 d+a+11 d+a+12 d = 141
3 a+33 d = 141
a+11 d = 47 (1)
now
sum of last three terms will be
a+22 d+a+21 d+a+20 d = 261 ( SINCE THERE ARE 23 TERMS SO (A+22D) IS THE LAST TERM )
a+21 d = 87 - (2)
now by solving 1 and 2
a = 3
so the correct option is D .
then given that there is 23 terms. so to find middle term of an Ap or median of ungrouped data we have
middle term = n+1/2 th term .
so 23+1/2 = 12
now ,
the three middle terms will be a+10 d , a+11 d , a+10 d
given - a+10 d+a+11 d+a+12 d = 141
3 a+33 d = 141
a+11 d = 47 (1)
now
sum of last three terms will be
a+22 d+a+21 d+a+20 d = 261 ( SINCE THERE ARE 23 TERMS SO (A+22D) IS THE LAST TERM )
a+21 d = 87 - (2)
now by solving 1 and 2
a = 3
so the correct option is D .
Answered by
3
Answer:
Step-by-step explanation:
Option - (D) 3
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