Question

Show that the progression 7, 2, -3, -ͺ, …..is an AP. Find its n term and its 6th term.


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Answer 1

CORRECT QUESTION:

Show that the progression 7, 2, -3, -8, …..is an AP. Find its n term and its 6th term.

ANSWER:

$\textsf{6 th term = -18}\\ \\ \textsf{nth term = 12 - 5n}$

GIVEN:

7, 2, -3, -8………………

a = 7

TO FIND:

$\textsf{ n^{th} term and 6^{th} term}$

TO PROVE:

The given terms are in A.P

FORMULAE:

$A_n = a + (n-1)d \\ \\ d = t_2 - t_1 = t_3 - t_2$

PROOF:

d = 2 - 7 = - 5

d = - 8 + 3 = - 5

The common difference is equal in both the ways. Hence showed that the terms are in A.P.

EXPLANATION:

We found d = - 5

$\displaystyle A_6 = 7 + (6 - 1)(-5)\\ \\A_6 = 7 + 5(-5)\\ \\A_6 = 7 -25\\ \\A_6 = - 18\\ \underline {\qquad \qquad \qquad \qquad\qquad \qquad \qquad \qquad }\\A_n = 7 + ( n - 1 )-5\\ \\A_n = 7 + -5n + 5\\ \\ A_n = 12 - 5n$

Answer 2

Step-by-step explanation:

✴️ QUESTION ✴️

Show that the progression 7, 2, -3, …..is an AP. Find its n term and its 6th term?

✴️ANSWER✴️

Formula used:

An=a+(n-1)d

d=a2-a1,a3-a2

✴️ SOLUTION ✴️

a=7

n=6

d=2-7=-5

=-3-2=-5

so,

common difference is -5

apply in formula

An=a+(n-1)d

A6=7+(6-1)-5

A6=7+(5)-5

A6=7-25

A6=-18

6 th of AP is -18