Question

The 7th term of an AP is 4 and its common difference is –4. What is its first term? ​

Answer 1

Given :

• $\sf\:a_7=4$
• common difference of an Ap is -4

To find :

First term of an Ap.

${\underline{\sf{Formula's}}}$

Genral term of an AP

$\sf\:T_{n}=a+(n-1)d$

•For an AP

$\sf\:T_{n}=S_{n}-S_{n-1}$

•Common difference of An AP is given by

$\sf\:d=S_{2}-2S_{1}$

Solution :

We have to find the first term of an Ap.

We know that ,Genral term of an AP

$\sf\:T_{n}=a+(n-1)d$

It is given that seventh term of an Ap is 4 and common difference = -4

$\sf\:a_7=a+6d$

$\sf\:4=a+6\times(-4)$

$\sf\:4=a-24$

$\sf\:a=24+4$

$\sf\:a=28$

Hence,The first term of an Ap is 28.

$\rule{200}2$

More About Arithmetic progression:

Sum of n terms of an Ap is given by :

$\sf\:S_{n}=\dfrac{n}{2}[2a+(n-1)d]$

Answer 2

$\sf{\underline{\underline{Question:-}}}$

The 7th term of an AP is 4 and its common difference is –4. What is its first term? 

$\sf{\underline{\underline{Formula:-}}}$

$\sf{\underline{\fbox{a_n=a+(n-1)d}}}$

★ where

$\sf→ a_n =7 \:or \:a_7\\\sf→ a= 1st\: term\\\sf→ n= given\: term \:or\: general\:term\\\sf→ d= common \: difference$

BY THE FORMULA

$\sf→ a_n= a+(n-1)d\\\sf→ 4=a+(7-1)*(-4)\\\sf→ 4= a+(6)×(-4)\\\sf→ a=-4-24\\\sf→ a=28$

$\sf{\underline{\underline{Hence:-}}}$

◆ 1st term will be =28