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Chapter 12: Q. 330 (page 1222)

Find the sum of the first 50terms of the arithmetic sequence whose general term is an=鈭�3n+100.

Short Answer

Expert verified

The sum of first50thterm of an arithmetic sequence is1175.

Step by step solution

01

Step 1. Given information

The sequence is as:

an=-3n+100

02

Step 2. Write the concept

The Sum Snof first n term of an arithmetic sequence is

Sn=n2a1+an

a1=firstterman=nthterm

03

Step 3. Calculation

Here, n=1,n=50to find the general term.

Therefore,

Whenn=1an=5n-1a1=-3(1)+100=-3+100=97Whenn=50a50=-3(50)+100=-150+100=-50

Now we use the sum formula and substitute the values:

a1=97a50=-50n=50S50=502(97-50)=25(47)=1175

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