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All the term of an A. P. are natural numbers and the sum of th

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All the term of an A. P. are natural numbers and the sum of the first $20$ terms is greater than $1072$ and less than $1162$ . If the sixth term is $32$ then-

First term is

12

First term is

7

Common difference is

4

Common difference is

5

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All the term of an A. P. are natural numbers and the sum of the first

20

terms is greater than

1072

and less than

1162

. If the sixth term is

32

then-

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Let Initial term

= a

, Diference

= d

a, d \in N

S_{20} = \frac{20}{2} [2 a + 19 d] = 10 (2 a + 19 d)

116.2 > 2 a + 19 d > 107.2

............ (1)

Also given

a + 5 d = 32

[Since sixth term so using formula for the

n t h

terms

a_{6} = a + 5 d

]

\Rightarrow a = 32 - 5 d

................ (2)

With

(1)

and

(2)

116.2 > 64 + 9 d > 107.2

∴ 52.2 > 9 d > 43.2

∴ d = 5

d \in N

a = 7

As the term in

A P

are natural numbers.

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Question Text	All the term of an A. P. are natural numbers and the sum of the first $20$ terms is greater than $1072$ and less than $1162$ . If the sixth term is $32$ then-
Answer Type	Text solution:1
Upvotes	150

All the term of an A. P. are natural numbers and the sum of the first 20 terms is greater than 1072 and less than 1162. If the sixth term is 32 then-

Text solutionVerified

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All the term of an A. P. are natural numbers and the sum of the first $20$ terms is greater than $1072$ and less than $1162$ . If the sixth term is $32$ then-