Question

in an ap if the common difference is -4 and the 7th term is 4.then find the first term​

Answer 1

Answer:

the first term is 36

Step-by-step explanation:

GIVEN :

common difference is -4

t7=4

n=7

by using formula

t^n=a+(n-1)d

t7=a+(7-1)-4

4=a+(6)-4

4=a+(-28)

4=a-28

a=4+28

a=32

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Answer 2

$\large\underline{Given:-}$

• 7th term of an Ap ⇢ 4
• Common difference ⇢ -4

$\large\underline{To find:-}$

• find the first term ...?

$\large\underline{Solutions:-}$

$\: \: \: \: \: \therefore \: \: \: {a_n} \: \: = \: \: {a} \: + \: {(n \: - \: {1})} \: d$

• a ⇢ ?
• d ⇢ -4
• n ⇢ 7
• an ⇢ 4

»★ We have

$\: \: \: \: \: \therefore \: \: {a_{n}} \: \: = \: \: {a} \: + \: {( n \: - \: 1)} \: d$

$\: \: \: \: \: \leadsto \: \: {4} \: \: = \: \: {a} \: + \: {( {7} \: - \: {1})} \: {-4}$

$\: \: \: \: \: \leadsto \: \: {4} \: \: = \: \: {a} \: + \: {( {6})} \: \times \: {-4}$

$\: \: \: \: \: \leadsto \: \: {4} \: \: = \: \: {a} \: + \: {( {-24})}$

$\: \: \: \: \: \leadsto \: \: {4} \: \: = \: \: {a} \: - \: {24}$

$\: \: \: \: \: \leadsto \: \: {-a} \: \: = \: \: {-24} \: - \: {4}$

$\: \: \: \: \: \leadsto \: \: {-a} \: \: = \: \: {-28}$

$\: \: \: \: \: \leadsto \: \: {a} \: \: = \: \: {28}$

$\: \: \: \: \: \: \: \: Hence,$

$\: \: \: \: \: \therefore {a} \: \: term \: \: is \: \: {28}$

$\large\underline{Basic \: Formula:-}$

• $\: \: \: \: \: {a_{n}} \: \: = \: \: {a} \: + \: {( n \: - \: 1)} \: d$

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

• $\: \: \: \: \: {S_{n}} \: \: = \: \: \frac{n}{2} \: {( {a} \: + \: {l})}$

$\large\underline{More \: Information:-}$

• a = first term.
• d = common difference.
• n = number of term.
• l = last term.
• an = nth term.

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