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Chapter 12: Q. 272 (page 1218)

In the following exercises, find the first term and common difference of the sequence with the given terms. Give the formula for the general term.

The third term is 鈭�26and the sixteenth term is 鈭�91.

Short Answer

Expert verified

The first term is -16and the common difference is -5.

The general term is an=-5n-11.

Step by step solution

01

Step 1. Given Information 

We are given that the third term is 鈭�26and the sixteenth term is 鈭�91.

We have to find the first term and common difference of a sequence.

02

Step 2. Finding the first term and common difference 

Let aa be the first term and dbe the common difference, so

a3=-26a+(3-1)d=-26a+2d=-26-(1)

Similarly, sixteenth term is given by,

a16=-91a+(16-1)d=-91a+15d=-91-(2)

03

Step 3. Solving the equations

Subtracting the second and first equation, we get

a-a+15d-2d=-91-(-26)13d=-91+2613d=-65d=-6513d=-5

Now, putting the value of din first equation, we get

a+2(-5)=-26a-10=-26a=-26+10a=-16

04

Step 4. Finding the general term 

Now, putting the value of first term and common difference in an=a1+(n-1)d,

an=-16+(n-1)(-5)an=-16-5n+5an=-5n-11

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