Question

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P​

Answer 1

Answer:

Let a is the first term and d is the common difference of an A.P.

Step-by-step explanation:

given

a+6d =. 49. eq (1)

a+16d =. 289 eq (2)

Subtracting eq 1 and 2

a. + 16d. =289

- a. + 6d. =49

therefore 10d =240

d. =24

putting the value of d in eq (1)

a + 6*24=49

a. = 49- 144

a. = -94

now ,

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

Sn. = n/2. [2(-94)+(n-1)(24)]

Sn. = n/2 [-188+24n-24]

Sn. = n/2 [-212+24n]

Sn. = 2n/2[-106+12n]

Sn. =. n[-106+12n]

Sn. = -106n. 12n^2

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