Question

Determine the expanded and simplified general term for the arithmetic sequence whose 5th term is 10 and consecutive terms decrease by 4.

Answer 1

Answer:

$a_{n}$ = - 6 + 4(n - 1)

Step-by-step explanation:

$a_{n}$ = $a_{1}$ + (n - 1)d

10 = $a_{1}$ + (5 - 1) × 4

$a_{1}$ = - 6

$a_{n}$ = - 6 + 4(n - 1)

Answer 2

Answer:

Required the expanded ans simplified general term is $a_n = - 6 + (n - 1) \times 4$

Step-by-step explanation:

Here we want to find the expanded and simplified general term for the arithmetic sequence whose 5th term is 10 and consecutive terms decrease by 4.

So,number of term is 10 and common difference between each term is 4.

We know,

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

Where $a_n$is the nth term and a is the 1st term and d is the common difference and n is number of terms.

By the given conditions,

$a_5 = a + (5 - 1) \times 4$

$10 = a + 4 \times 4$

$10 = a + 16$

We are separating variable and constant part,

$a = - 16 + 10 = - 6$

The expanded and simplified general term for the arithmetic sequence whose 5th term is 10 and consecutive terms decrease by 4 is $a_n = - 6 + (n - 1) \times 4$

Where n is the number of terms.

One another formula of Arithmetic

progression,

1.Sum of First n Terms $= \frac{n}{2}$(1st term+last term)