Step-by-step explanation:
Given Arithmetic series is:
7+13+19+25+...+ 85
Here,
First term a = 7
Common Difference d = 13 - 7 = 6
last term [tex] t_n= 85[/tex]
First let us find the number of terms in given series.
[tex] t_n= a + (n-1)d\\
\therefore 85 = 7+ (n-1)\times 6\\
\therefore 85 = 7+ 6n-6\\
\therefore 85 = 1+ 6n\\
\therefore 6n = 85 - 1
\therefore 6n = 84
\therefore n = \frac{84}{6}\\
\therefore n = 14\\
[/tex]
Hence, given series has total 14 terms.
Sum of n terms of an Arithmetic series is given as:
[tex]S_n = \frac{n}{2} (a + t_n) \\ \\ \therefore \: S_{14}= \frac{14}{2} \times \: (7 + 85) \\ \\ \therefore \: S_{14}= 7 \times \: 92 \\ \\ \huge \red{ \boxed{\therefore \: S_{14}= 644 }}\\ [/tex]
