T6=T4+2d, so 2d=12
Now you can find T1=a, and then T7
the Fourth term of an a.p is 37 and the 6th term is 12 more than the Fourth term.find the first and seventh terms
2 answers
a4 = 37
a6 = a4 + 12
a6 = 37 + 12 = 49
In an arithmetic progression nth term of the sequence (an) is given by:
an = a1 + ( n - 1 ) d
so:
a4 = a1 + ( 4 - 1 ) d = 37
a1 + 3 d = 37
a6 = a1 + ( 6 - 1 ) d = 49
a1 + 5 d = 49
Now you must solve system of two equations with two unknowns :
a1 + 3 d = 37
a1 + 5 d = 49
a1 + 3 d = 37 Subtract 3 d to both sides
a1 + 3 d - 3 d = 37 - 3 d
a1 = 37 - 3 d
a1 + 5 d = 49
37 - 3 d + 5 d = 49
37 + 2 d = 49 Subtract 37 to both sides
37 + 2 d - 37 = 49 - 37
2 d = 12 Divide both sides by 2
d = 6
a1 + 5 d = 49
a1 + 5 * 6 = 49
a1 + 30 = 49 Subtract 30 to both sides
a1 + 30 - 30 = 49 - 30
a1 = 19
a7 = a1 + ( 7 - 1 ) d
a7 = 19 + 6 d
a7 = 19 + 6 * 6
a7 = 19 + 36
a7 = 55
a6 = a4 + 12
a6 = 37 + 12 = 49
In an arithmetic progression nth term of the sequence (an) is given by:
an = a1 + ( n - 1 ) d
so:
a4 = a1 + ( 4 - 1 ) d = 37
a1 + 3 d = 37
a6 = a1 + ( 6 - 1 ) d = 49
a1 + 5 d = 49
Now you must solve system of two equations with two unknowns :
a1 + 3 d = 37
a1 + 5 d = 49
a1 + 3 d = 37 Subtract 3 d to both sides
a1 + 3 d - 3 d = 37 - 3 d
a1 = 37 - 3 d
a1 + 5 d = 49
37 - 3 d + 5 d = 49
37 + 2 d = 49 Subtract 37 to both sides
37 + 2 d - 37 = 49 - 37
2 d = 12 Divide both sides by 2
d = 6
a1 + 5 d = 49
a1 + 5 * 6 = 49
a1 + 30 = 49 Subtract 30 to both sides
a1 + 30 - 30 = 49 - 30
a1 = 19
a7 = a1 + ( 7 - 1 ) d
a7 = 19 + 6 d
a7 = 19 + 6 * 6
a7 = 19 + 36
a7 = 55