Question

solve both questions.
No IRRELEVANT ANSWERS PLZZ.​

Answer 1

S O L U T I O N :

Case (I), Find the fourth term from the end in an AP -11, -8 , -5 ,.......... 49.

Explanation :

AP = -11 , -8 , -5 ,......... 49.

Here,

• First term (a) = -11
• Common difference (d) = -8 + 11 = 3
• tn = 49

nth term of AP is given as ;

↪ tn = a + (n - 1)d

[ Put the values ]

↪49 = -11 + (n - 1) × 3

↪49 = -11 + (3n - 3)

↪ 49 = -11 + 3n - 3

↪ 49 = -14 + 3n

↪ 49 + 14 = 3n

↪ 63 = 3n

↪ n = 21

Given that, we need to find the fourth term from the end in an AP.

↪ 21 - 4

↪ 17

Now,

↪ t_17 = -11 + (17 - 1) × 3

↪ t_17 = -11 + 16 × 3

↪ t_17 = -11 + 48

↪ t_17 = 37

Therefore,

The fourth term from the end in an AP is 37.

_______________

Case (II), Find the sum of all even numbers for 1 to 350.

Explanation :

AP :- 2 ,4 , 6, ........ 350

Here,

• First term (a) = 2
• Common difference (d) = 4 - 2 = 2
• tn = 350

nth term of an AP,

↪ tn = a + (n - 1)d

[ Put the values ]

↪ 350 = 2 + (n - 1) × 2

↪ 350 = 2 + 2n - 2

↪ 350 = 2n

↪ n = 175

Now,

Sum of nth term of an AP,

↪ Sn = n/2 [ 2a + (n - 1)d ]

[ Put the values ]

↪ S_175 = 175/2 [2 × 2 + (175 - 1) × 2]

↪ S_175 = 175/2 [4 + 174 × 2]

↪ S_175 = 175/2 [350]

↪ S_175 = 175 × 175

↪ S_175 = 30625

Therefore,

The sum of all even numbers for 1 to 350 is 30625.