Question

In an arithematic sequence
with 10 terms, 5th and 6th terms
are 17 and 20. If so, find
the sum
of first 10 terms​

Answer 1

$\huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}$

Given that,

• a5 = 17
• a6 = 20

We can write these terms as,

• a5 → a + 4d = 17 ..... (1)
• a6 → a + 5d = 20 ..... (2)

Subtract the equations (1) & (2). We get,

➡ - d = - 3

➡ d = 3

$\boxed{∴ d = 3 }$

Substitute the value of d in equation (1)

➡ a + 4(3) = 17

➡ a + 12 = 17

➡ a = 17 - 12

➡ a = 5

$\boxed{∴ a = 5 }$

We should find the sum of 10 terms. Now, we have

• a = 5
• d = 3
• n = 10
• Sn = ?

☯ Sn = n/2 [ 2a + (n - 1)d ]

➡ S10 = 10/2 [ 2(5) + (10 - 1)(3) ]

➡ S10 = 5 [ 10 + (9)3 ]

➡ S10 = 5 [ 10 + 27 ]

➡ S10 = 5[37]

➡ S10 = 185

$\underline{\boxed{\bf{\purple{∴ Sum\;of\;10\;terms\;is\;“ \: 185 \: " }}}}$

Step-by-step explanation:

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