Mixed Questions on Arithmetic Progression :
Worksheet given in this section will be much useful for the students who would like to recall the concepts in arithmetic progression.
Question 1 :
For an AP, given that a = 7 and d = 3. Find the 8th term.
Solution:
From the given details we have to find nth term
an = a + (n - 1) d
an = 7 + (8 - 1) (3)
a8 = 7 + 7 (3)
a8 = 7 + 21
a8 = 28
Hence the required term is 28.
(ii) a = -18, n = 10, an = 0 find the common difference.
Solution :
we need the find the common difference
an = 0
a + (n - 1) d = 0
-18 + (10 - 1) d = 0
-18 + 9 d = 0
9 d = 18
d = 2
(iii) d = -3 n = 18 an = -5, find the first term.
Solution :
an = -5
a + (n - 1) d = -5
a + (18 - 1) (-3) = - 5
a + 17 (-3) = -5
a - 51 = -5
a = -5 + 51
a = 46
(iv) a = -18.9, d = 2.5 and an = 3.6. Find the value of n.
Solution :
an = 3.6
a + (n - 1) d = 3.6
-18.9 + (n - 1) (2.5) = 3.6
(n -1) 2.5 = 3.6 + 18.9
(n - 1) 2.5 = 22.5
n - 1 = 22.5/2.5
n - 1 = 9
n = 9 + 1
n = 10
(v) a = 3.5,d = 0 and n = 105. Find the general term.
Solution :
an = a + (n - 1) d
an = 3.5 + (105 - 1) 0
an = 3.5 + 104 (0)
an = 3.5
After having gone through the stuff given above, we hope that the students have recalled all the concepts in arithmetic progression.
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