Question

in an arithmetic progression , if a = -18.9 , d= 2.5 , An = 3.6 then find n ...​

Answer 1

Answer:

n = 10

Step-by-step explanation:

We know, An= a + (n-1)d

by this,

3.6 = -18.9 + (n-1)2.5

3.6 + 18.9 = (n-1)2.5

22.5= (n-1)2.5

22.5÷2.5 = n-1

9= n-1

9+1= n

10 = n

Answer 2

Given

• in an arithmetic progression , if a = -18.9 , d= 2.5 , An = 3.6

To Find

• Value of n

SOLUTION

We have an ap in which

• a=-18.9
• d=2.5
• $\rm \: a_{n} = 3.6$

We have an Formula to find an that is

$\rm \: a_{n} = a + (n - 1)d \\ \\ \bf \: putting \: values \\ \\ \rm 3.6 = - 18.9 + (n - 1)2.5 \\ \\ \implies \rm 3.6 + 18.9 = (n - 1)2.5 \\ \\ \rm \implies \: 22.5 = (n - 1)2.5 \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \rm \: \frac{22.5}{2.5} = n - 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \rm \: 9 = n - 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \underline{\huge{ \boxed{ \bf \: n = 10}} }\: \:$

Hence the value of n is 10

Verification

$\rm a_{n} = a + (n - 1)d \\ \\ \implies \rm \: RHS = - 18.9 + (10 - 1) \times 2.5 \\ \\ \implies \rm \: RHS = 22.5 - 18.9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \underline{ \boxed{ \huge{ \bf \: RHS = 3.6 =LHS }}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf hence \: proved$

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