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Chapter 12: Q. 58 (page 817)

How many terms must be added in an arithmetic sequence whose first term is 78 and whose common difference is -4 to obtain a sum of 702?

Short Answer

Expert verified

Number of terms either 27 or 13

Step by step solution

01

Given information 

In an arithmetic sequence,

first term is 78 , a1=78

common difference is -4, d=-4

sum is 702

02

Sum formula 

Sn=n22a1+(n-1)d702=n22(78)+(n-1)(-4)multiplyby2onbothsides1404=n(156-4n+4)1404=-4n2+160n4n2-160n+1404=0

03

Quadratic formula 

Solve for n using quadratic formula

4n2-160n+1404=0n=--160卤-1602-4路鈥�4路鈥�14042路鈥�4n=--160卤鈥�568n=--160+鈥�568=27n=--160-鈥�568=13

Number of terms either 27 or 13

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