Question

the 13 term of an ap is 4 times in 3 term if the 5 term 16 term then the sum of its first term is ​

Answer 1

given a13=4a3, a5=16

an=a+(n−1)d

a13=a+12d

a3=a+2d

∴a+12d=4(a+2d)

=> 3a=4d

=> a=4/3d

a5=a+4d

16=4/3d+4d

48=16d=>d=3

a=4

Sn=n[2a+(n−1)d]/2

S10=10[2(4)+(9)(3)] /2

= =5[8+27]

= =5×35=175

Hence the sum of first ten term is 175