Question

Please help!!!!!!

The 7th term of one sequence is 7 and the 17th term is 37. The 9th term of another sequence is -8, and the 29th term is -88. The two sequences have an equal term. Find this term.

Answer 1

Answer:

a7=7 , a17 = 37

a+6d=7....(i) , a+16d = 37.....(ii)

From (i) and (ii)

a+6d=7

a+16d=37

subtract (i) and (ii)

-10d= -30

d=3

put d=3 in first we get a=-11

NOW in second case,

a'9=-8 , a'29=-88

a'+8d'=-8...... (iii) , a'+28d'=-88... (iv)

From (iii) and (iv),

a'+8d'=-8

a'+28d'=-88

subtract (iii) and (iv)

-20d'=80

d'= -4

putting d' in (iii)

a' = 24

NOW,

an=a'n'

a+(n-1) d = a'+(n-1) d'

-11+(n-1) (3) = 24+(n-1) (-4)

-11+3n-3=24-4n+4

-14+3n=28-4n

3n+4n=28+14

7n =42

n= 6

HENCE 6th term of the given A.P.'s are equal.