Question

(b) Check whether - 321 is a term of the A.P.: 22, 15, 8, 1,.......​

Answer 1

Answer:

AP = a + (n-1)d

-321 = 22 + (n-1)(-7)

-7n+7= - 343

-7n = - 340

n = 48.57

because n is not a whole number

Step-by-step explanation:

Answer 2

Given:-

• AP = 22, 15, 8, 1,.......$\sf a_n$

To prove:-

• -321 is a term of this AP

Solution:-

• a = 22
• d = (15 - 22) = -7

Lets -321 is the last term ( $\sf a_n$) of this AP.

Identity used:-

$\bold{\underline{\underline{\boxed{\sf{\purple{\dag \; \sf a_n = a + (n - 1)d}}}}}}$

Put values in formula:-

$\implies \sf{-321 = 22 + (n - 1)(-7)}$

$\implies \sf{-321 = 22 + (n - 1)(-7)}$

$\implies \sf{-321 - 22 = -7n + 7}$

$\implies \sf{-343 - 7 = -7n}$

$\implies \sf{-350 = -7n}$

$\implies \sf{ \cancel{ \dfrac{-350}{-7}} = n}$

$\implies \bold{\underline{\underline{\boxed{\sf{\blue{\dag \; n = 50}}}}}}$

Therefore, -321 is the 50th term of AP.

$\rule{200}{2}$