The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?
any ideas please?
any ideas please?
now Arithmetic progression sum formula
s=(n/2)(2*a+(n-1)d)
a= first term
d= common difference
term of an AP t=a+(n-1)d
t(4)=a+3d
t(12)=a+11d
given t(4)+t(12)=20
a+3d+a+11d=20
2a+14d=20 ------( equation 1)
we know
s=(n/2)(2*a+(n-1)d)
s=(15/2)(2a+(15-1)d) (taking n as 15 as we need to find sun of 15 terms)
s=(15/2)(2a+14d)
s=(15/2)*20 (replacing value of 2a+14d from equation 1)
s=150
