Question

8. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18
respectively.
9. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of
first n terms.
251​

Answer 1

8. Given, n= 51
a2= 14
a3= 18
To find- S51
Solution-
We know that, a2= a+d
a3= a+2d
So,
a+d= 14 - equation 1
a+2d=18 - equation 2
- - -
-d= -4
d=4.
Substituting value of d in equation 1, we’ll get,
a+4=14
a= 14-4
a= 10.
Now,
Sn=n/2 [2a+ (n-1) d]
So, S51= 51/2 [2(10) + (51-1) 4]
= 51/2 [20+ (50)(4)]
= 51/2[ 20+ 200]
= 51/2 [220]
= 51 * 110
Answer= 5,610.

Answer 2

Answer:

Step-by-step explanation:

 Given, n= 51

a2= 14

a3= 18

To find- S51

Solution-

We know that, a2= a+d

a3= a+2d

So,

a+d= 14 - equation 1

a+2d=18 - equation 2

- - -

-d= -4

d=4.

Substituting value of d in equation 1, we’ll get,

a+4=14

a= 14-4

a= 10.

Now,

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

So, S51= 51/2 [2(10) + (51-1) 4]

= 51/2 [20+ (50)(4)]

= 51/2[ 20+ 200]

= 51/2 [220]

= 51 * 110

Answer= 5,610.