Question

if the sum of the first 15 terms of an automatic progression is 240 what is it 8 th term​

Answer 1

Step-by-step explanation:

Let a be the first term and d be the common difference of the given A.P. Then,

S6=42⟹26{2a+(6−1)d}=42⟹2a+5d=14      ...(i)

It is given that

a10:a30=1:3

⟹a+29da+9d=31

⟹3a+27d=a+29d

⟹2a−2d=0

⟹a=d                         ...(ii)

putting the value of a in (i), we get

2d+5d=14⇒d=2 

 ∴a=d=2

∴a13=a+12d=2+2×12=26

Hence, first term =2 and thirteenth term =26