Question
The 14th Term Of An Ap Is 98 While The 25th Term Is 173.Find A)19th Term B)13th Term C)56th Term
Answers
In AP:
an = a ( n - 1 ) d
where
a = first term
d = common difference
a14 = a + 13 d = 98
a25 = a + 24 d = 173
Now find:
a25 - a14
a + 24 d = 173
-
a + 13 d = 98
______________
11 d = 75
d = 75 / 11
Put this value in:
a + 13 d = 98
a + 13 • 75 / 11= 98
a + 975 / 11 = 98
Multiply both sides by 11
11 a + 975 = 1078
Subtract 975 to both sides.
11 a = 103
a = 103 / 11
______________
a19 = a + 18 d
a13 = a + 12 d
a56 = a + 55 d
Calculate this.
a19 = 1453 / 11
a13 = 1003 / 11
a55 = 4153 / 11
an = a ( n - 1 ) d
where
a = first term
d = common difference
a14 = a + 13 d = 98
a25 = a + 24 d = 173
Now find:
a25 - a14
a + 24 d = 173
-
a + 13 d = 98
______________
11 d = 75
d = 75 / 11
Put this value in:
a + 13 d = 98
a + 13 • 75 / 11= 98
a + 975 / 11 = 98
Multiply both sides by 11
11 a + 975 = 1078
Subtract 975 to both sides.
11 a = 103
a = 103 / 11
______________
a19 = a + 18 d
a13 = a + 12 d
a56 = a + 55 d
Calculate this.
a19 = 1453 / 11
a13 = 1003 / 11
a55 = 4153 / 11