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Cerrena [4.2K]
3 years ago
9

Find the sum of first 20 to terms of an ap in which d is equal to 7 and 20 second term is 149​

Mathematics
2 answers:
GuDViN [60]3 years ago
6 0

Answer:

1370

Step-by-step explanation:

<h3>Given</h3>
  • AP with d= 7 and a₂₂ = 149
<h3>To find</h3>
  • Sum of first 20 terms
<h3>Solution</h3>

<u>First, let's get the value of the first term:</u>

  • aₙ = a + (n-1)d
  • a₂₂ = a + 21d
  • 149 = a + 21*7
  • a = 149 - 147
  • a= 2

<u>Next, let's find the sum of the first 20 terms</u>

  • Sₙ = 1/2n(2a+ (n-1)d)
  • S₂₀ = 1/2*20(2*2 + 19*7) = 10(4 + 133) = 10*137 = 1370

<u>Answer is</u> 1370

Likurg_2 [28]3 years ago
5 0

Answer:

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

We've to find out the sum of 20 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}}}. \\

<h2>______________________</h2>

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 \lgroup a + l\bigg \rgroup}

Where :

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

:\implies\sf S_{22} = \dfrac{\cancel{20}}{\cancel{\:2}} \bigg(2 + 149 \bigg) \\\\\\:\implies\sf S_{22} = 10 \times 151 \\\\\\:\implies\boxed{\frak{\purple{ S_{22} = 1510}}}

\therefore\underline{\textsf{ Hence, Sum of 20 terms of the AP is \textbf{1510}}}. \\

<h3>⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀</h3>

⠀

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