The sum of the arithmetic series: a1 = 9, a3 = 17, s5 =?

a1 = 9. eq1

a2 = 17. eq2

Firstly we have to find d

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

a+a+2d = 17 +9

18 + 2d = 26. [we have a = 9]

2d = 8

d = 4

Now we have to find a5

a5 = a+(n-1)d

a5 = 9 + (5-1)4

a5 = 25

now we can easily find s5

s5 = n\2(a+l)

s5 =5\2(9+25)

s5 = 85

Check

s5 = a1 + a2 + a3 +a4 +a5

s5 = 9 +13+17+21+25= 85

Hope it helps