Question

А.п. -4;2;0 найти:S10​

Answer 1

а₁=-4

а₂=2

а₃=0

d=а₂-а₁=а₃-а₂=2

а₁₀=а₁+9d=-4+9·2=22

S₁₀=(1/2)(a₁+а₁₀)·10=5·(2+22)=120

Answer 2

To find the nth term of an arithmetic progression (AP), you can use the formula:

$a_n = a_1 + (n-1)d$

where: $a_n$ = nth term $a_1$ = first term $d$ = common difference (the difference between consecutive terms)

In your case, you provided the first three terms of the arithmetic progression: -4, 2, and 0.

Step 1: Find the common difference (d). $d = a_2 - a_1 = 2 - (-4) = 6$

Step 2: Find the first term (a_1). To find the first term, you can use any of the given terms. Let's use the second term (2) and the common difference (6): $a_1 = a_2 - (n-1)d = 2 - (2-1)6 = 2 - 6 = -4$

Now we have the first term (a_1 = -4) and the common difference (d = 6). We can use the formula to find the nth term (S10) of the arithmetic progression when n = 10:

$S_{10} = a_1 + (10-1)d$ $S_{10} = -4 + 9 \cdot 6$ $S_{10} = -4 + 54$ $S_{10} = 50$

The 10th term (S10) of the arithmetic progression is 50.