SECTION A 1. The sum of the 2nd and 5th terms of an arithmetic progression (A.P) is 42. If the difference between the 6th and 3rd terms is 12, find: a. the ...
Question 1 Report
SECTION A
1. The sum of the 2nd and 5th terms of an arithmetic progression (A.P) is 42. If the difference between the 6th and 3rd terms is 12, find:
a. the common difference
b. the first term
c. the 20th term.
Answer Details
a. fifth term, T\(_5\) =? But the nth term of an A.P. T\(_n\) = a (n - 1) d
T\(_2\) = a + d
T\(_3\) = a + 2d
T\(_5\) = a + 4d
T\(_2\) + T\(_5\) = a + d + a + 4d = 2a + 5d = 42 .....(i)
T\(_6\) = a + 5d
T\(_3\) = a + 2d
T\(_6\) - T\(_3\) = (a + 5d) - (a + 2d) = 3d = 12
3d = 12
d = 4
b. put d = 4 into equation (i)
2a + 5(4) = 42
2a = 42 - 20
2a = 22
a = 11 first term,
a = 11
c. T\(_{20}\) = a + 19d
= 11 + 19 x 4
T\(_{20}\) = 87.
Download The App On Google Playstore
Everything you need to excel in your exams
