Question

Algebraic expression of an arithmetic sequence is 5n+3 .a) find 20th term.b) find sum of first 38 term

Answer 1

Answer:

a) 103

b) 8+193

201

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Answer 2

$\large{\boxed{\bf{Answer}}}$

3417

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Given :-

• Algebraic expression of an arithmetic sequence is 5n + 3.

To Find :-

• It's 20th term and sum of 1st 38 terms.

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$\large{\boxed{\bf{Solution}}}$

• first term T1, a = 5(1) + 3 = 5 + 3 = 8

• second term, T2 = 5(2) + 3 = 10 + 3 = 13

∴ common difference, d = T2 - T1 = 13 - 8 = 5

For finding nth term of an AP, the formula is :-

Tn = a + (n - 1)d

T20 = 8 + (20 - 1)5

T20 = 8 + 95

T20 = 103

Hence, the value of 20th term is 103.

For finding sum of nth terms of an AP, the formula is :-

Sn = n/2 {2a + (n - 1)d}

S38 = 38/2 {2(8) + (38 - 1)5}

S38 = 17 {16 + 185}

S38 = 17 × 201

S38 = 3417

∴ The sum of 38 terms is 3417.

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