Question

PLS ANSWER it CORRECTLY for 25 points​

Answer 1

Answer:

1. 0

2. 18 th term

3. 209

4. 670

Step-by-step explanation:

1. n^th term  of an A.P = a + (n - 1)d , where n is the term

6 = a + (5 - 1)d ... (i)

5 = a + (6 - 1)d ... (ii)

a + 4d = 6 ... (i)

a + 5d = 5 ... (ii)

Subtracting (ii) - (i) we get;

0 + d = -1 , d = -1

So the common difference (d) = -1

And first term (a);

a + 4(-1) = 6

a = 6 + 4 = 10

11^th term will be;

$n_{11}$ = 10 + -1(11 - 1) = 10 - 10 = 0

2. The A.P is;

1, 4, 7, 10, 14, ....

The first term (a) = 1

The common difference (d) = 3

$n_{th}$ = a + (n - 1)d

52 = 1 + (n - 1)3

3n - 3 + 1 = 52

3n = 52 + 2 = 54

n = 54/3 = 18 th term

3. The A.P is;

4, 9, 14, ... , 254

The first term (a) = 4

The common difference (d) = 5

$n_{th}$ = a + (n - 1)d

To find what term number 254 is;

254 = 4 + (n - 1)5

5n - 5 + 4 = 254

5n = 254 + 1 = 255

n = 255/5 = 51

The 10^th term from the end of the AP is the 42^nd term.

$n_{42}$ =  4 + (42 - 1)5 = 4 + 205 = 209

4. The A.P is;

5, 8, 11, 14, ...

The first term (a) = 5

The common difference (d) = 3

Sum of n terms in an A.P is given by;

$s_{n}$ = $\frac{n}{2}$(2a + (n - 1)d)

$s_{n}$ = $\frac{20}{2}$(10 + 19(3) = 10(10 +57) = 670