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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±192-4· 3-21842· 3n=-19± 1636n=-19+ 1636=24n=-19- 1636=-913

number of terms cannot be negative

So, n= 24

24 terms added to obtain a sum of 1092

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Most popular questions from this chapter

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.

a1=2;an=-an-1

In Problems 17–28, write down the first five terms of each sequence.

sn=43n

In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

9+12+16+643+....

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.

1,-2,3,-4,5,-6,...

In Problems 17–28, write down the first five terms of each sequence.

Sn=2n3n+1
See all solutions

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