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 391 respectively, then the sum of the first 10 terms of the AP is A 410 B 205 C 381 D 340

Answer 1

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

`a_(n)=a_(1)+(n-1)d`

`a_n` = the nᵗʰ term in the sequence

`a_1` = the first term in the sequence

`d` = 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