The terms of the arithmetic progression are given a1 = –15, a2 = –12.1. Find the difference of the arithmetic progression

The terms of the arithmetic progression are given a1 = –15, a2 = –12.1. Find the difference of the arithmetic progression. 2. Write down the formula for the nth term of this progression. 3. Find a10.4. Find out if there is a member equal to 33 in this progression. If so, what is its number?

In the arithmetic progression an, the first two terms are given:

a1 = –15;
a2 = –12.
1. Calculate the difference in the progression:

a2 = a1 + d;
d = a2 – a1 = -12 + 15 = 3.
2. Let’s find the formula for the n-th term:

an = a1 + (n – 1) d;
an = -15 + (n – 1) * 3 = -15 + 3n – 3 = 3n – 18.
3. The tenth term of the progression is equal to:

a10 = a1 + (10 – 1) * d = -15 + 9 * 3 = -15 + 27 = 12.

4. Find the number of the term equal to 33:

an = 33;
3n – 18 = 33;
3n = 33 + 18;
3n = 51;
n = 51: 3;
n = 17.
Answer:

13;
2) an = 3n – 18;
3) a10 = 12;
4) a17 = 33.