Question

In an AP,if the common difference (d)=-4,and the seventh term (a7)is 4, then find the first term.

Answer 1

Answer:

First term (a) = 28

Explanation:

Given in an A.P

common difference (d)=-4---(1)

Let first term = a

/* we know that ,

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

*/

Now,

$a_{7} = 4$

/* given */

=> a + 6d = 4

=> a + 6(-4) = 4 [ from (1)]

=> a - 24 = 4

=> a = 28

Therefore,

First term (a) = 28

••••

Answer 2

First term of the AP series is 28.

Solution:

According to the arithmetic progression the formula to find nth term is $\bold{T_{n}=a+(n-1)d}$

a = first term in the series.

n = number of terms present in the series.

$T_{n}$= the term that is to be found out or given.

d = the common difference between two numbers of the series.

Now putting the value of d = -4 and $a_{7}$ = 4,

we get 4=a+(7-1)(-4)

a = 28.