Question

the first term of an A.P is 30 and 24 if sn =84 find the value of n​

Answer 1

Answer:

a = 30, d = 24-30= -6

Sn = n/2[2a+(n-1)d]

84 = n/2 [2×30+(n-1)-6]

84= n/2[60-6n+36]

84=n/2[96-6n]

84=n[48-3n]

3n^2-48n+84=0

3(n^2-16n+28)=0

n^2-14n-2n+28=0

n(n-14) -2(n-14)=0

(n-14) (n-2) =0

n=14 and 2

Answer 2

FOR A.P

•A SEQUENCE IS SAID TO BE AN ARITHMETIC PROGGRESION ( AP ) IF THE DIFFERENCE BETWEEN IT'S CONSECUTIVE TERMS ARE EQUAL.

•THE NTH TERM OF THE AP IS GIVE BY A(N) = A + (N - 1)D WHERE A IS THE FIRST TERM AND D IS THE COMMON DIFFERENCE.

•THE COMMON DIFFERENCE OF THE AP IS GIVEN BY A2 - A1 = D .

•IF THE NO. OF TERMS OF THE AP OS ODD THEN THERE WILL BE A SINGLE MIDDLE TERM AND IT IS GIVEN BY (N + 1)/2

•IF THE NO. OF TERMS OF THE AP OS EVEN THEN THERE WILL BE A TWO MIDDLE TERM AND IT IS GIVEN BY (N)/2 AND (N/2 + 1) .

•THE SUM UP TO NTH TERM O AN AP IS GIVEN BY S(N) = N/2[2A + (N - 1)D] WHERE A IS THE FIRST TERM AND NI IS THE NO. OF TERMS.

•THE NTH TERM OF THE AP IS ALSO CALCULATED AS T(N) = S(N) - S(N - 1)

GIVEN :-

THE FIRST TWO TERM 30 AND 24 AND S(N) = 84

TO FIND:-

VALUE OF N

METHOD USED:-

THE FORMULA TO CALCULATE D AND S(N)

SOLUTION:-

AS WE ARE GIVEN WITH,

A1 = 30

A2 = 24

THEN D = A2 - A1

D = 24 - 30 = - 6

AND IF S(N) = 84

S(N) = N/2[2A + (N - 1)D]

HERE GIVEN , N = ?

S(N) = 84

D = -6

A = 30

SO PUTTING IN FORMULA,

84 = N/2 [ 2×30+(N -1)-6]

168 = N[60 -6N +6]

168 = 66N -6N²

N² - 11N + 28 = 0

(N-7)(N-4)

SO N = 7 OR N = 4

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