Question

В арифметической прогрессии S5=40; S10=155 найти S16

Answer 1

S5=s1+4d
S10=S1+9d
-5d=-115
d=23
s1=40-(4*23)=-52
s16=s1+15d=-52+15*23=293

Answer 2

Arithmetic Progression Problem

To find the value of S16 in the arithmetic progression given that S5 = 40 and S10 = 155, we can use the formula for the sum of an arithmetic progression:

Sn = n/2 * (a1 + an)

Where: - Sn is the sum of the first n terms - a1 is the first term - an is the nth term

First, let's find the common difference (d) and the first term (a1).

Finding the Common Difference (d)

We can use the formula for the nth term of an arithmetic progression to find the common difference: an = a1 + (n - 1)d

Using the given values: 1. S5 = 40 2. S10 = 155

We can find the common difference (d) by subtracting S5 from S10 and then dividing by 5: d = (S10 - S5) / (10 - 5)

Finding the First Term (a1)

Once we have the common difference, we can find the first term (a1) using the formula for the nth term: an = a1 + (n - 1)d

We can rearrange this formula to solve for a1: a1 = an - (n - 1)d

Calculating S16

Now that we have the common difference and the first term, we can use the formula for the sum of an arithmetic progression to find S16: S16 = 16/2 * (a1 + a16)

Let's calculate d, a1, and then find S16.