Determine an AP whose third term is 16 and when fifth term is subtracted from 7th term we get 12.
NO SPAMMING
Answers
Answer:
10,16,22,28,34,40,......
Step-by-step explanation:
given:-
In AP,
Let 1st term be a and common difference be d
t3 = 16
t7-t5 = 12
we know,
tn = a+(n-1)d
t3 = a+(3-1)d
16 = a + 2d
a + 2d = 16 -----------(eq 1)
t7 = a+(7-1)d
t7 = a+6d
t5 = a+(5-1)d
t5 = a+4d
ATQ,
t7-t5 = 12
(a+6d) - (a+4d) = 12
a+6d-a-4d = 12
2d = 12
d = 12/2
d = 6
putting the value in equation 1,
a + 2d = 16
a + 12 = 16
a = 16-12 = 4
a = 4
t1 = a = 4
t2 = a+d = 4+6 = 10
t3 = a+2d = 4+12 = 16
t4 = a+3d = 4+18 = 22
t5 = a+4d = 4+24 = 28
t6 = a+5d = 4+30 = 34
t7 = a+6d = 4+36 = 40
verification,
t3 = a+2d = 4+12 = 16
t7-t5 = 40-28 = 12
Step-by-step explanation:
Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof.