Question

if the sum of an ap ia 7&13th trm is 35 find the sum of first 13 term

Answer 1

tn=a+(n-1)d

t7=a+(7-l)d
t7=a+6d

t13=a+(13-1)d
t13=a+12d

t7+t13=35
a+6d+a+12d=35
2a=35-18d
a=35/2-9d

Sum of first 13 terms(Sn) =n/2(2a+(n-1)d)

S13=13/2(2a+(13-1)d)
S13=13/2(2×[35/2-9d]+12d)
S13=13/2(35-18d+12d)
S13=13/2(35-12d)
S13=455/2-6d