[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
[tex]\blue\star[/tex]a1 = 9. eq1
[tex]\blue\star[/tex]a2 = 17. eq2
Firstly we have to find d
[tex]\blue\star[/tex]d = a2 -a1
we dont have a2 so we can do this by other method
split a3 into a+2d
Now add equation 1 and 2
[tex]\blue\star[/tex] a+a+2d = 17 +9
[tex]\blue\star[/tex] 18 + 2d = 26. [we have a = 9]
[tex]\blue\star[/tex] 2d = 8
[tex]\blue\star[/tex] d = 4
Now we have to find a5
[tex]\blue\star[/tex] a5 = a+(n-1)d
[tex]\blue\star[/tex] a5 = 9 + (5-1)4
[tex]\blue\star[/tex] a5 = 25
now we can easily find s5
[tex]\blue\star[/tex]s5 = n\2(a+l)
[tex]\blue\star[/tex] s5 =5\2(9+25)
[tex]\blue\star[/tex] s5 = 85
[tex]\huge\boxed{S5 = 85}[/tex]
Check
s5 = a1 + a2 + a3 +a4 +a5
s5 = 9 +13+17+21+25= 85
Hope it helps
The sum of the arithmetic sequence [tex]S_5=85[/tex]
Explanation :
Arithmetic series, a1 = 9, a3 = 17
We need to find out sum of 5 terms
The formula to find sum of arithmetic series is
[tex]S_n=\frac{n}{2} (2a+(n-1)d)[/tex]
where 'a' is the first term
'd' is the common difference and n is the number of terms
a1=9,, first term is 9
formula for nth term is [tex]a_n=a_1+(n-1)d[/tex]
a3=17, it means third term is 17
lets find out 'd' using third term
[tex]a_3=a_1+(3-1)d\\17=9+2d\\17-9=2d\\8=2d\\d=4[/tex]
So value of d=4
Now use sum formula to find out S5
[tex]S_n=\frac{n}{2} (2a+(n-1)d)\\n=5, d=4, a_1=9\\\\S_5=\frac{5}{2} (2(9)+(5-1)4)\\S_5=\frac{5}{2}\cdot \:34\\S_5=85[/tex]
Learn more : brainly.com/question/12733379
