Problem Solving

A computer generated a consecutive set of numbers 'A' using the following formula: An = A1 + (n-1)*d, where d is the common difference between any two consecutive numbers of set 'A.' If the sum of the second and the fifth number in the set is 8, and the sum of the third and the seventh number is 14, what is the first number in set 'A'?

A) 3
B) 2
C) 1
D) -1
E) -3

OA: D

a sequence with numbers in the form of An = A1 + (n-1)*d where, d is the common difference, is called Arithmetic progression.
according to the question: a2 +a5 = 8
ie. a+d+a+4d=8 => 2a + 5d = 8 ---- (1)

a3+ a7 = 14
ie 2a+ 8d = 14 ---- (2)

solving both the equations:

we get d= 2 and a= -1

hence we get a = -1.

Answer option: D

Hope this helps!

An=A1+(n-1)d

A2=A1+d
A5=A1+4d

A2+A5=8---->2A1+5d=8.........(1)

A3=A1+2d
A7=A1+6d
A3+A7=14---->2A1+8D=14.....(2)

USING EQN 1 AND 2

D=2
A1=-1
HENCE D