Question

find the sum of 51. Term of AP whose second term and third term are 14 and 18 respectively​

Answer 1

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Answer 2

Given a2=14 and a3=18
a2=14
a+d=14......(1)
also,a3=18
a+2d=18......(2)
now solve both by elimination method
a+d=14
a+2d=18
-. -. -
-------------
-d=-4
-------------
d=4
Put d in (1)
a+d=14
a+4=14
a=14-4
a=10

TO FIND SUM OF 51=
Sn=n/2[2a+(n-1)d]
S51=51/2[2(10)+(51-1)(4)]
S51=51/2[20+50(4)]
S51=51/2[20+200]
S51=51/2(220)
S51=51×100
S51=5610

Therefore, sum of 51 terms is 5610