Question

How many terms of the A.P 5,7,9.....have to be added to get the sum 320​

Answer 1

Answer:

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Sequences and Series

Arithmetic Progression

How many terms of the A.P, ...

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Asked on December 20, 2019 by

Aamir Spoorthi

How many terms of the A.P,3,5,7,9,−−−−− must be added to get the sum of 120?

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ANSWER

120=

2

n

[a+a+(n−1)d]

where n= no of terms 

           a=first term

           d=common difference

120=

2

n

[3+3+(n−1)2]

240=n[3+3+(n−1)2]

240=n[6+2n−2]

240=n[4+2n]

n

2

+2n−120=0

n

2

+12n−10n−120=0

n(n+12)−10(n+12)=0

(n−10)(n+12)=0

n=10

no of terms must be added 10−4=6 terms

Answer 2

Answer:

16

Step-by-step explanation:

a=5

d=2

Sn=320

Sn=n/2(2a+(n-1)d)

320= n/2(2×5+(n-1)2)

320=n/2(10+2n-2)

320=n/2(8+2n)

320×2=n(8+2n)

640=8n+2n²

8n+2n²-640=0

2(n²+4n-320)=0

n²+4n-320=0

n²+20n-16n-320

n(n+20)-16(n+20)

(n-16)(n+20)

n=16,-20(Not possible)

so,the answer is 16