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Chapter 12: Q. 57 (page 817)

How many terms must be added in an arithmetic sequence whose first term is 11 and whose common difference is 3 to obtain a sum of 1092?

Short Answer

Expert verified

24 terms added to obtain a sum of 1092

Step by step solution

01

Given information 

first term is 11 , a1=11

common difference is 3 , d=3

sum is 1092

02

sum formula

Sum of n terms formula is

Sn=n22a1+(n-1)dsubstituteallthevaluesinsidetheformula1092=n22(11)+(n-1)3solveforn1092=n222+3n-3multiplyby2onbothsides2184=n(3n+19)2184=3n2+19n3n2+19n-2184=0

03

solve for n 

applyquadraticformulatosolvefornn=-19卤192-4路鈥�3-21842路鈥�3n=-19卤鈥�1636n=-19+鈥�1636=24n=-19-鈥�1636=-913

number of terms cannot be negative

So, n= 24

24 terms added to obtain a sum of 1092

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