When n arithmetic mean is inserted between 25 and 37, the sum of all the terms is 651. Then the value of n is?

n = 21

Step-by-step explanation:

since we are told that n arithmetic mean are inserted between 25 and 37, then;

the first term is 25

The nth term of an arithmetic progression is expressed as:

Tn = a+(n-1)d

a is the first term

d is the common difference

n is the number of terms

The sum Sn = n/2[a+l]

Given

a = 25

Tn = 25+(n-1)d

Sn = n/2(25+37)

Sn = n/2(62)

Sn = 31n

Since the sum of the terms is 651, then:

651 = 31n

n = 651/31

n = 21

Hence the value if n is 21

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step-by-step explanation:

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step-by-step explanation: