Question

if a 1= 32 and a7= 8 then find the 4th term of the arithmetic sequence

Answer 1

Solution

• aₙ = a + (n - 1)d

→ a₁ = a + (1 - 1)d

→ a₁ = a = 32

→ a₇ = a + (7 - 1)d

→ a₇ = a + 6d

→ 8 = 32 + 6d

→ - 4 = d

→ a₄ = a + (4 - 1)d

→ a₄ = a + 3d

→ a₄ = 32 + 3(- 4)

→ a₄ = 32 - 12

→ a₄ = 20

Answer: 20

Answer 2

Arithmetic sequence :

An Arithmetic sequence or progression is the one in which, next term is found by adding a specific number.

Say, First term a,

Say, First term a, U can add some "d" to get second term " a + d".

From the given data,

$a_1 = 32 \: \\ a_7 = 8$

Some useful general information about AP is,

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

Now,

$a_1 = a = 32$

For 7th term,

$a_7 = 8 = a + (7 - 1)d = a + 6d$

What is the term we need to find?

Fourth term

$a_4 = a + (4 - 1)d = a + 3d$

I would write it as,

$a_4 = \frac{a_1 + a_7}{2}$

Why?

$\frac{a_1 + a_7}{2} = \frac{a + (a + 6d)}{2} = \frac{2a + 6d}{2} = a + 3d$

Now,

$a_4= \frac{8 + 32}{2} = \frac{40}{2} = 20$

Therefore, 4th term of this Arithmetic progression is 20