Question

if the sum of 12th and 22nd terms of an AP is 100 find the sum of first 33 terms

Answer 1

GIVEN:
a12 + a22= 100
[an= a+(n-1)d]
a12= a+(12-1)d
a12= a+11d…………..(1)

a22= a+(22-1)d
a22= a+21d……………(2)

a12 + a22= 100
a+11d + a+21d=100
[ From eq 1 & 2]
2a+32d= 100
2(a+16d)= 100
a+16d= 50……………..(3)

Sn= n/2[2a+(n-1)d]
S33= 33/2[2a+(33-1)d]
S33= (33/2)[(2a+32d)]
S33= (33/2)[2(a+16d)]
S33= 33(a+16d)
S33= 33(50)
[From eq 3]
S33= 1650
Hence, the sum of the first 33 terms is S33= 1650

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