Question

find AP sequence,whose third term is 16 and seventh term exceds the 5 th term by 12

Answer 1

t3=16 ........................(given).........(1)
we know that ,
tn=a+(n-1)d
we get,
t3=a+2d...........................................(2)
from (1) &(2)
a+2d=16...........................................(3)
by the given condition

t7=t5+12

we know that tn=a+(n-1)d
using the formula we get

t7=a+6d
t5=a+4d
substitute this in the given condition

a+6d=a+4d+12

6d=4d+12
6d-4d=12
2d=12
d=12/2

we get,
d=6

substitute d=12 in equation number (3).

a+2d=16
a+2(6)=16
a+12=16
a=4

NOW WE ARE FREE TO FIND THE ARITHMETIC PROGRESSION(A .P)

t1=a=4

t2=a+d=4+6=10
t2=10

t3=16........................(given)

t4=a+3d=4+3(6)=22
t4=22

REQUIRED A .P:
4,10,16,22...............

$hope \: this \: helps$