Question

The sum of first 15 term arithmetic sequence is 570 and 12th term is 62 write its sequence

Answer 1

Answer:

All we have to do now is to apply the formula sn=n2(2a+(n−1)d)) to determine the sum of the sequence. Thus, the sum of the first fifteen terms in the arithmetic sequence is 975 .

Step-by-step explanation:

Answer 2

Answer:

Let the first term of the required A.P be 'a' and its common difference be 'd'

Given : S15= 570

t12= 62

To find : The A.P.

Solution:

S15 = 570........( Given)

We know that,

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

So,

S15= 15/2 [2a+(15-1)d]

570= 15 /2[2a +14d]

570= 15(a+7d) ....... [ By taking 2 common and cancelling)

a+7d= 38........ (1)

But,

t12= 62

we know that,

tn = a+(n-1)d

so,

t12= a+ (12-1)d

a+11d= 62......... (2)

By (2)- (1), we get

a+11d=62

a+7d=38

- - -

________

4d= 24

d=6

Substituting the value of d in equation (1) , we get

a+ 7(6) = 38

a+ 42= 38

a= 38-42

a= -4

The required A.P. can be represented as

(a-d), a, (a+d),(a+2d) ,..................

-10,-4,2,8,................... is the required A.P

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