Question

How to solve this? ​

Answer 1

Answer:

First term = 28

Step-by-step explanation:

Given : Common difference, d = - 4

Seventh term, ${\sf{a_7}}$ = 4

To Find : First term, a

${\boxed{\sf{\red{Formula \ : \ a_n = a + (n - 1)d}}}}$

Putting n = 7, we get

→ ${\sf{a_7 = a + (7 - 1)d}}$

Putting known values, we get

→ ${\sf{4 = a + (7 - 1)(- 4)}}$

→ ${\sf{4 = a + (6)(- 4)}}$

→ ${\sf{4 = a - 24}}$

→ ${\sf{a = 4 + 24}}$

→ a = 28

• An arithmetic progession (AP) is a sequence of numbers such that the difference between the consecutive numbers is constant.

Answer 2

Given,

The common difference of the AP is - 4

• $\sf{d = - 4}$

The seventh term of the AP is 4

• $\sf{{a}_{7} = 4}$

To finD

First term of the AP

The nth term of an AP is given by :

$\boxed{ \sf{ {a}_{n} = a + (n - 1)d}}$

Putting n = 7,

$\sf{ {a}_{7} = a + 6d }$

→ $\sf{4 = a + 6( - 4)}$

→ $\sf{a = 24 + 4}$

→ $\boxed{ \boxed{ \sf{a = 28}}}$

The first term of the above sequence is 28