# Find the sum of the first 22 terms of the AP 1,4,7,10,…. ?

Answer

Verified

379.5k+ views

Hint- Here, we will be using the formula for the sum of first n terms of an arithmetic progression (AP) which is ${{\text{S}}_n} = \dfrac{n}{2}\left[ {2{a_1} + \left( {n - 1} \right)d} \right]$ and in order to get the sum of the first 22 terms of the given AP, we will evaluate ${{\text{S}}_{22}}$ by substituting n=22.

Complete step-by-step answer:

The given AP series is 1,4,7,10,….

Clearly, the first term of the given series is ${a_1} = 1$

Here, common difference is $

d = 4 - 1 \\

\Rightarrow d = 3 \\

$

As we know that the sum of first n terms of an AP series having first term as ${a_1}$ and common difference as d is given by

${{\text{S}}_n} = \dfrac{n}{2}\left[ {2{a_1} + \left( {n - 1} \right)d} \right]$

Now for the sum of the first 22 terms of the given AP series, we will put n=22, ${a_1} = 1$ and d=3 in the above formula.

$

{{\text{S}}_{22}} = \dfrac{{22}}{2}\left[ {2\left( 1 \right) + 3\left( {22 - 1} \right)} \right] \\

\Rightarrow {{\text{S}}_{22}} = 11\left[ {2 + 63} \right] \\

\Rightarrow {{\text{S}}_{22}} = 715 \\

$

Therefore, the sum of the first 22 terms of the given AP series is 715.

Note- An arithmetic progression (AP) is the series which will have the same common difference between any two consecutive terms like in the given series the common difference is constant between any two consecutive terms i.e., 3. For any general AP, the formula for ${n^{th}}$ term of this AP is given by ${a_n} = {a_1} + \left( {n - 1} \right)d$.

Complete step-by-step answer:

The given AP series is 1,4,7,10,….

Clearly, the first term of the given series is ${a_1} = 1$

Here, common difference is $

d = 4 - 1 \\

\Rightarrow d = 3 \\

$

As we know that the sum of first n terms of an AP series having first term as ${a_1}$ and common difference as d is given by

${{\text{S}}_n} = \dfrac{n}{2}\left[ {2{a_1} + \left( {n - 1} \right)d} \right]$

Now for the sum of the first 22 terms of the given AP series, we will put n=22, ${a_1} = 1$ and d=3 in the above formula.

$

{{\text{S}}_{22}} = \dfrac{{22}}{2}\left[ {2\left( 1 \right) + 3\left( {22 - 1} \right)} \right] \\

\Rightarrow {{\text{S}}_{22}} = 11\left[ {2 + 63} \right] \\

\Rightarrow {{\text{S}}_{22}} = 715 \\

$

Therefore, the sum of the first 22 terms of the given AP series is 715.

Note- An arithmetic progression (AP) is the series which will have the same common difference between any two consecutive terms like in the given series the common difference is constant between any two consecutive terms i.e., 3. For any general AP, the formula for ${n^{th}}$ term of this AP is given by ${a_n} = {a_1} + \left( {n - 1} \right)d$.

Recently Updated Pages

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How many meters are there in a kilometer And how many class 8 maths CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

What were the major teachings of Baba Guru Nanak class 7 social science CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a labelled sketch of the human eye class 12 physics CBSE