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The common difference of an arithmetic progression (AP) is 3, and the common ratio of a geometric progression (GP) is 5. Corresponding terms of the AP and GP are added to form a new sequence. If the first and the fourth terms of this sequence are 10 and 391, respectively, then find the sum of the first 10 terms of the AP.

A. 410
B. 205
C. 381
D. 340

Answer :

The sum of the first 10 terms of the AP is B 235.

How the sum of the first 10 terms of the AP is computed using the following formula:

Sₙ = n/2 (2a+(n−1)d)

Where:

Sₙ = Sum of the AP series

n = the number of terms

a = the value of the first term

d = the common difference

Common Difference of AP = 3

Common Ratio of a GP = 5

First term of the AP, a = 10

Fourth term of the AP, = 19

Therefore, the sum of the AP is given as:

= 10/2 (2 x 10 + (10 - 1)3)

= 5 (20 + (9)3)

= 5 (20 + 27)

= 235

Check:

Formula

[tex]a_{n}=a_{1}+(n-1)d[/tex]

[tex]a_n[/tex] = the nᵗʰ term in the sequence

[tex]a_1[/tex] = the first term in the sequence

[tex]d[/tex] = the common difference between terms

Alternatively, we can use the above check formula to find all the terms and sum manually.

Complete Question:

The common difference of an arithmetic progression is 3 and the common ratio of a geometric prepression is 5.Corresponding terms of the AP and GP is added form a new sequence. If the first and the fourth arms of this sequence are 10 and 19 respectively, then the sum of the first 10 terms of the AP is A 410 B 235 C 381 D 340

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Rewritten by : Barada