Question

The sum of first 16 terms of an A.P is 112 and sum of next 14 terms is 518. Find The A.P

Answer 1

Sum of an AP is given by the equation:
\[SUM _{n}=\frac{n}{2} ( a _{1} +a _{n})\]

substitute all the numbers,

Sum of first 16 terms= 16/2 ( a1 + a16)=112
a1+a16= 14 ---(1)

Sum of (16+14=) 30 terms = 30/2 (a1+a30)= 518+112
630=30/2 (a1+a30)
a1+a30 = 42 ---(2)

take eqn(2) minus eqn(1)

a1+a30 - a1-a16 = 42-14
a30-a16= 28
a1 + 29d - a1 - 15d = 28
since the term is defined by the equation \[a _{n}=a _{1} +\left( n -1 \right)d\]

29d-15d=28
14d= 28
d=2

if d=2 and the Sum of first 16 terms= 16/2 ( a1 + a16)=112
a1+a16 = 14
a1 +a1 + 15d = 14
2 a1+ 15(2) = 14
2a1 = -16
a1 = -8

The first term is -8 and the common difference is 2

Answer 2

looks like people are getting stingy with medals these days :/

Answer 3

all that work and not even a courteious thanx ... well I appreciate all the effort you put into it :)

Answer 4

haha i dun really mind! i just want to help out. I explain so much, so i hope they understand and learn by themselves. They should treat this website as somewhere to learn instead of just copying all their questions in their homework here to get quick answers.