Question

The sum of the 4^th and 8^th terms of an AP is 24 and the sum of its 6^th and 10^th terms is 44. Find the sum of its first 10 terms.   

Answer 1

Let a be the first and d be the common difference of the AP.

∴ a₄ + a_s = 24                        (Given)

⇒ ( a +3d) + (a +7d) = 24                  [ a_n = a +(n-1) d ]

⇒ 2a + 10d = 24 

⇒ a + 5d = 12                         ...................(1)

Also, 

∴ a₆ + a₁₀ = 44                      (Given)

⇒ (a +5d) + (a + 9d) = 44               [ a_n = a + (n-1)d] 

⇒ 2a + 14 d = 44

 ⇒  a + 7d = 22                   ................(2)

Subtracting (1) from (2), we get

(a + 7d) - (a + 5d) = 22-12 

⇒  2d = 10 

⇒  d= 5

Putting d = 5 in (1), we get

a +5 × 5 =12

⇒ a = 12-25 = -13 

`"Using the formula," S_n = n/2 [ 2a +(n-1) d] ,`we get

`S_10 = 10/2 [ 2 xx (-13 ) + (10-1) xx5]`

= 5 × (-26 + 45)

= 5 ×  19 

=95 

Hence, the required sum is 95.