a. First five terms: 9,13,17,21,25
b. Sum of first 25 terms = 1425
c. The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.
Further explanation:
Given
Formula of sequence
[tex]a_n=4n+5[/tex]
1. First 5 terms:
For first 5 terms, we have to put n=1,2,...5,
So,
[tex]For\ n=1\\a_1=4(1)+5\\=4+5\\=9\\For\ n=2\\a_2=4(2)+5\\=8+5\\=13\\For n=3\\a_3=4(3)+5\\=12+5\\=17\\For\ n=4\\a_4= 4(4)+5\\=16+5\\=21\\For\ n=5\\a_5=4(5)+5\\=20+5\\=25\\First\ 5\ terms\ are: 9,13,17,21,25[/tex]
2. Sum of first 25 terms:
For that we have to find 25th term first
[tex]a_{25} = 4(25)+5\\=100+5\\=105[/tex]
The formula for sum is:
[tex]S_n=\frac{n}{2}(a_1+a_n)}\\Putting\ the\ values\\S_n=\frac{25}{2}(9+105)\\=12.5(114)\\=1425[/tex]
3. Type of sequence
The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.
i.e.
[tex]d=4[/tex]
Keywords: Arithmetic sequence, Sum of arithmetic sequence
Learn more about arithmetic sequence at:
- brainly.com/question/3280369
- brainly.com/question/7221312
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