Question

find 17th term of 2,13,24,35

Answer 1

Your answer:

Here, a = 2, d = ? and a₁₇ = ?

Let's first find d

a₁ = 2

a₂ = 13

d = a₂ - a₁

d = 13 - 2 = 11

d = 11

aₙ = a + (n - 1) d

a₁₇ = 2 + (17 - 1) 11

= 2 + (16) 11

= 2 + 176

a₁₇ = 178

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Answer 2

Arithmetic Progression

We will use the concept of AP to solve the problem.

AP - A sequence of numbers in which common difference between two consecutive terms is always same.

In an AP with first term $a$ and common diffence $d$, then $nth$ term is given by,

$\longrightarrow T_n = a + (n - 1) d$

Where,

• Tₙ - the value at a particular term
• a - the first term
• n - the number of terms
• d - the common diffence

If we have any three known values in the above mentioned formula, we can find the unknown value.

Solution:

According to the question information, we have been given that,

• First term, a = 2
• Second term, a₂ = 13
• Common diffence, d = a₂ - a = 13 - 2 = 11
• Number of term, n = 17
• 17th term, T₁₇ = ?

By using the formula of nth term and substituting the known values in it, we obtain the following results:

$\implies T_n = a + (n - 1) d$

$\implies T_{17} = 2 + (17 - 1) 11$

$\implies T_{17} = 2 + 16 \times 11$

$\implies T_{17} = 2 + 176$

$\implies \boxed{T_{17} = 178}$

Hence, the 17th term of the AP is 178.

$\rule{300}{2}$

Important formulae

1. In an AP with first term $a$ and common diffence $d$, then $nth$ term is given by,

$\longrightarrow \boxed{T_n = a + (n - 1) d}$

2. Let $a$ be the first term, $d$ be the common difference and $l$ be the last term if an AP. Then nth term from the end is given by,

$\longrightarrow \boxed{\rm{nth \; term \; from \; the \; end} = \it{l - (n - 1) d}}$

3. The sum of $n$ terms of an AP in which first term $a$, common diffence $d$ and last term $l$ is given by,

$\longrightarrow \boxed{S_n = \dfrac{n}{2} (a + l)}$