Question

Find the sum of first 22 terms of an A.P in which d=7 and 22nd term is 149?????

Answer 1

AnswEr :

$\frak{Given}\begin{cases} \sf{\: Common \: difference \: (d) = 7}\\\sf{ \: 22nd \ term = 149} \end{cases}$

We've to find out the sum of 22 terms. So, n = 22

By using nth term Formula of the AP :

$\star \ \boxed{\sf{\purple{a_{n} = a + (n -1)d}}}$

$\underline{\bf{\dag} \:\mathfrak{Substituting \ Values \ in \ the \ formula \ :}}$

$:\implies\sf 149 = a + (22 - 1) \times 7 \\\\\\:\implies\sf 149 = a + 21 \times 7 \\\\\\:\implies\sf 149 = a + 147\\\\\\:\implies\sf a = 149 - 147\\\\\\:\implies\boxed{\frak{\purple{a = 2}}}$

$\therefore\underline{\textsf{ Here, we get value of the First term (a) of AP \textbf{2}}}.$

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For any Arithmetic Progression ( AP ), the sum of n terms is Given by :

$\bf{\dag}\quad\large\boxed{\sf S_n = \dfrac{n}{2}\bigg(a + l\bigg)}$

Where :

• n = no. of terms
• a = First Term
• l = Last Term

$:\implies\sf S_{22} = \dfrac{\cancel{22}}{\cancel{\:2}} \bigg(2 + 149 \bigg) \\\\\\:\implies\sf S_{22} = 11 \times 151 \\\\\\:\implies\boxed{\frak{\purple{ S_{22} = 1661}}}$

$\therefore\underline{\textsf{ Hence, Sum of 22 terms of the AP is \textbf{1661}}}.$

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$\qquad\qquad{\underline{\underline{\dag \: \bf\:Formulaes \ of \: the \:AP\: :}}}$⠀⠀

• To find out the nth term of the AP $\sf\pink{a_n + (n - 1)d}$⠀⠀⠀

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• To find out the Sum of the AP = $\sf\purple{S_n = \dfrac{n}{2} \bigg[\sf 2a + (n - 1)d \bigg]}$⠀

• To find out the sum of all terms have the last term of the AP 'l' = $\sf \blue{\dfrac{n}{2}(a + l)}.$

Answer 2

Answer:

1661

Step-by-step explanation:

• Given: AP with d= 7 and a₂₂ = 149

• To find: Sum of first 22 terms

Solution :

First, let's get the value of the first term:

↬ aₙ = a + (n-1)d

↬ a₂₂ = a + 21d

↬ 149 = a + 21*7

↬ a = 149 - 147

↬ a= 2

Next, let's find the sum of the first 22 terms :

↬ Sₙ = n/2(a + l)

↬ S₂₂ = 22/2(2 + 149)

↬ S₂₂ = 11(151)

↬ S₂₂ = 1661

Answer is 1661