Question

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

Answer 1

`\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) * 7 \\\\\\:\implies\sf 149 = a + 21 * 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 = (n)/(2)\bigg \lgroup a + l\bigg \rgroup}`

Where :

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

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

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

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Answer 2

1370

Explanation:

Given

• AP with d= 7 and a₂₂ = 149

To find

• Sum of first 20 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 20 terms

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

Answer is 1370