Question

in an AP,IF THE COMMON DIFFERENCE IS -4 AND THE SEVENTH TERM IS 4 FIND THE FIRST TERM

Answer 1

Answer:

First term in given A.P

First term in given A.P = a = 28

Explanation:

Given,

In an A.P ,

common difference(d)=-4

Let first term = a

$\boxed { n^{th} term\:(a_{n})= a+(n-1)d}$

Now ,here

n = 7

$7^{th}\:term = 4$

\* given *\

$\implies a+6d=4$

Substitute d = -4 in above equation, we get

$\implies a+6\times(-4)=4$

$\implies a-24=4$

$\implies a= 4+24$

$\impies a = 28$

Therefore,

First term in given A.P

= a = 28

••••

Answer 2

The value of first term 'a' is 28

Step-by-step explanation:

Given Data

In an Arithmetic Progression ,

Common Difference (d) = -4

Seventh term = 4

To find the first term (a)

The formula to find the nth term is $a_n = a + (n-1) d$

When n = 7,

$a_7 = a +(7-1) (-4)$

$a_7 = a +(6) (-4)$

$a_7 = a - 24$

where $a_7 = 4$

4 = a - 24

a = 4 + 24

a = 28

The value of first term 'a' is 28 when the common difference and seventh term in an Arithmetic Progression is -4 and 4. The Arithmetic Progression series can be written as (24,28,32,..,etc.,) (a-d, a, a+d,..,etc.,)

To Learn More ....

1)In an ap the 10th term is 46 sum of the 5th and 7th term is 52 find the ap

https://brainly.in/question/4200699

2)If 7 times the 7th term of an A.P is equal to the 12 times the 12th term, then find its 19th term

https://brainly.in/question/7644506