Question

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Answer 1

Question:

The first and last term of AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is theri sum?

Answer:

The number of terms of the AP is 38.

The sum of the first 38 terms of the AP is 6973.

Step-by-step-explanation:

We have given that,

The first and last term of an AP are 17 & 350 respectively.

The common difference of the AP is 9.

We have to find the number of terms and their sum.

Here,

• a = t₁ = 17
• tₙ = l = 350
• d = 9

Now, we know that,

tₙ = a + ( n - 1) * d - - [ Formula ]

⇒ 350 = 17 + ( n - 1 ) * 9

⇒ 350 = 17 + 9n - 9

⇒ 350 = 17 - 9 + 9n

⇒ 350 = 8 + 9n

⇒ 9n = 350 - 8

⇒ 9n = 342

⇒ n = 342 ÷ 9

⇒ n = 38

Now, we know that,

Sₙ = ( n / 2 ) [ a + l ] - - [ Formula ]

⇒ S₃₈ = ( 38 / 2 ) [ 17 + 350 ]

⇒ S₃₈ = 19 * 367

⇒ S₃₈ = 6973

∴ The number of terms of the AP is 38.

The sum of the first 38 terms of the AP is 6973.

Answer 2

Number of terms in A.P is 38.

Sum of numbers in A.P is 6973.

Question :-

The first and last term of A.P are 17 and 350 respectively. If the

common difference is 9. How many terms are there and what is sum?

Given :-

First term of the A.P (a) = 17

Last term of the A.P (l) = 350

Common difference (d) = 9

To Find :-

Find number of terms (n) and Sum of term (Sn)

Formulas Applied :-

$n = ( \frac{l - a}{d} ) + 1$

$s_{n} =( \frac{n}{2}) (a + l)$

Solution :-

As by the formula let's find the number of terms (n)

$n = ( \frac{l - a}{d} ) + 1$

$n = ( \frac{350 - 17}{9} ) + 1$

$n = ( \frac{333}{9} ) + 1$

$n = 37 + 1 \\ n = 38$

Now Find the value of sum of terms (Sn) by given formula ,

$s_{38} = ( \frac{n}{2} )(a+ l)$

$s_{38} = (\frac{38}{2} )(19 + 350)$

$s_{38} = (19)(367)$

$s_{38} = 6973$