Question

please answer this question ​

Answer 1

Answer:

your answer is 5610

Step-by-step explanation:

you can find the explanation in the pic

Answer 2

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GiveN:

• Second term of the AP = 14
• Third term of the AP = 18

To FinD:

• Sum of 51 terms of the AP....?

Step-wise-Step Explanation:

According to question, The 2nd term is 14. 2nd term in terms of a and d can be written as:

• a + d = 14 ------------(1)

The 3rd term is 18. So, 3rd term in terms of a and d can be written as:

• a + 2d = 18 ------------(2)

Subtracting (2) from (1),

⇒ a + 2d - (a + d) = 4

⇒ a + 2d - a - d = 4

⇒ d = 4

Putting value of d in equation-1)

⇒ a + 4 = 14

⇒ a = 10

Now we have got the value of a and d. Sum of 51 terms can be found by using Formula:

$\rm{ \underline{ \boxed{ \rm{sn = \frac{n}{2} \bigg(2a + (n - 1)d \bigg)}}}}$

Putting the values of a, d and n:

⇒ S51 = 51/2 { 2(10) + (51 - 1)4 }

⇒ S51 = 51/2 { 20 + 200 }

⇒ S51 = 51/2 { 220 }

⇒ S51 = 51 × 110

⇒ S51 = 5610

Thus, the required sum of 51 terms of the AP is 5610.