Question

Question 5 Find the number of terms in each of the following A.P.
I. 7, 13, 19, …, 205
II. 18, 15.1/2, 13, ..., -47

Class 10 - Math - Arithmetic Progressions Page 106

Answer 1

(i) For this A.P.,
a = 7
d = a2 − a1 = 13 − 7 = 6
Let there are n terms in this A.P.
an = 205
We know that
an = a + (n − 1) d 
Therefore, 205 = 7 + (n − 1) 6
198 = (n − 1) 6
33 = (n − 1) 
n = 34
Therefore, this given series has 34 terms in it.

(ii) For this A.P.,
a = 18

d = a² - a¹ = 15½ - 18

d = 31 - 36 / 2 = -5/2

Let there are n terms in this A.P.
an = 205

an = a + (n − 1) d

-47 = 18 + (n - 1) (-5/2)

-47 - 18 = (n - 1) (-5/2)
-65 = (n - 1)(-5/2)
(n - 1) = -130/-5
(n - 1) = 26
n = 27
Therefore, this given A.P. has 27 terms in it.

Answer 2

HI !

1) 7 , 13 , 19 ..... 205

first term = a = 7
common difference = d = 6
last term = an = 205

no: of terms = n

an = a + ( n - 1) d
205 = 7 + ( n - 1) 6
205 - 7 = 6n - 6
198 = 6n - 6
198 + 6 = 6n
204 = 6 n

n = 34

NO: of terms = n = 34
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2) 18, 15.1/2, 13, ..., -47

first term = a = 18

common difference = d = 15 1/2 - 18 = -5/2


last term = an = -47

an = a + (n − 1) d

-47 = 18 + (n - 1) -5/2

-47 - 18 = (n - 1) -5/2

-65 = (n - 1)(-5/2)

(n - 1) = -130/-5

(n - 1) = 26

n = 27


NO: of terms = n = 27