Given that 7, 11, 15, 19, ... is an arithmetic progression, find the (a) tenth term, (b) sum of the first…

Question

Given that 7, 11, 15, 19, ... is an arithmetic progression, find the (a) tenth term, (b) sum of the first twelve terms.

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Given the arithmetic progression 7, 11, 15, 19, . Step 1: Identify the first term (a) and the common difference (d). The first term is a = 7. The common difference is d = 11 − 7 = 4. a) Find the tenth term. Step 2: Use the formula for the n-th term of an arithmetic progression, u_n = a + (n−1)d. For the tenth term, n=10. u₁₀ = 7 + (10−1)4; u₁₀ = 7 + (9)4; u₁₀ = 7 + 36; u₁₀ = 43 The tenth term is 43. b) Find the sum of the first twelve terms. Step 3: Use the formula for the sum of the first n terms of an arithmetic progression, S_n = n/2(2a + (n−1)d). For the sum of the first twelve terms, n=12. S₁₂ = 12/2(2(7) + (12−1)4); S₁₂ = 6(14 + (11)4); S₁₂ = 6(14 + 44); S₁₂ = 6(58); S₁₂ = 348 The sum of the first twelve terms is 348.

Given that 7, 11, 15, 19, ... is an arithmetic progression, find the (a) tenth term, (b) sum of the first twelve terms.

Answers

Step-by-step solution

Part a· 1 step

Use the formula for the $n$ -th term of an arithmetic progression, $u_n = a + (n-1)d$ .

Part b· 1 step
$\text{348}$

Use the formula for the sum of the first $n$ terms of an arithmetic progression, $S_n = \frac{n}{2}(2a + (n-1)d)$ .

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Given that 7, 11, 15, 19, ... is an arithmetic progression, find the (a) tenth term, (b) sum of the first twelve terms.

Answers

Step-by-step solution

Part a· 1 step

Use the formula for the nnn-th term of an arithmetic progression, un=a+(n−1)du_n = a + (n-1)dun​=a+(n−1)d.

Part b· 1 step348\text{348}348

Use the formula for the sum of the first nnn terms of an arithmetic progression, Sn=n2(2a+(n−1)d)S_n = \frac{n}{2}(2a + (n-1)d)Sn​=2n​(2a+(n−1)d).

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Still stuck on this one?

More Mathematics Questions

Use the formula for the $n$ -th term of an arithmetic progression, $u_n = a + (n-1)d$ .

Part b· 1 step
$\text{348}$

Use the formula for the sum of the first $n$ terms of an arithmetic progression, $S_n = \frac{n}{2}(2a + (n-1)d)$ .